---
_id: '16527'
author:
- first_name: S.
  full_name: Day, S.
  last_name: Day
- first_name: O.
  full_name: Junge, O.
  last_name: Junge
- first_name: K.
  full_name: Mischaikow, K.
  last_name: Mischaikow
citation:
  ama: Day S, Junge O, Mischaikow K. A Rigorous Numerical Method for the Global Analysis
    of Infinite-Dimensional Discrete Dynamical Systems. <i>SIAM Journal on Applied
    Dynamical Systems</i>. 2004:117-160. doi:<a href="https://doi.org/10.1137/030600210">10.1137/030600210</a>
  apa: Day, S., Junge, O., &#38; Mischaikow, K. (2004). A Rigorous Numerical Method
    for the Global Analysis of Infinite-Dimensional Discrete Dynamical Systems. <i>SIAM
    Journal on Applied Dynamical Systems</i>, 117–160. <a href="https://doi.org/10.1137/030600210">https://doi.org/10.1137/030600210</a>
  bibtex: '@article{Day_Junge_Mischaikow_2004, title={A Rigorous Numerical Method
    for the Global Analysis of Infinite-Dimensional Discrete Dynamical Systems}, DOI={<a
    href="https://doi.org/10.1137/030600210">10.1137/030600210</a>}, journal={SIAM
    Journal on Applied Dynamical Systems}, author={Day, S. and Junge, O. and Mischaikow,
    K.}, year={2004}, pages={117–160} }'
  chicago: Day, S., O. Junge, and K. Mischaikow. “A Rigorous Numerical Method for
    the Global Analysis of Infinite-Dimensional Discrete Dynamical Systems.” <i>SIAM
    Journal on Applied Dynamical Systems</i>, 2004, 117–60. <a href="https://doi.org/10.1137/030600210">https://doi.org/10.1137/030600210</a>.
  ieee: S. Day, O. Junge, and K. Mischaikow, “A Rigorous Numerical Method for the
    Global Analysis of Infinite-Dimensional Discrete Dynamical Systems,” <i>SIAM Journal
    on Applied Dynamical Systems</i>, pp. 117–160, 2004.
  mla: Day, S., et al. “A Rigorous Numerical Method for the Global Analysis of Infinite-Dimensional
    Discrete Dynamical Systems.” <i>SIAM Journal on Applied Dynamical Systems</i>,
    2004, pp. 117–60, doi:<a href="https://doi.org/10.1137/030600210">10.1137/030600210</a>.
  short: S. Day, O. Junge, K. Mischaikow, SIAM Journal on Applied Dynamical Systems
    (2004) 117–160.
date_created: 2020-04-15T08:17:18Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1137/030600210
language:
- iso: eng
page: 117-160
publication: SIAM Journal on Applied Dynamical Systems
publication_identifier:
  issn:
  - 1536-0040
publication_status: published
status: public
title: A Rigorous Numerical Method for the Global Analysis of Infinite-Dimensional
  Discrete Dynamical Systems
type: journal_article
user_id: '15701'
year: '2004'
...
---
_id: '16587'
abstract:
- lang: eng
  text: <jats:p> We discuss nearest neighbor load balancing schemes on processor networks
    which are represented by a cartesian product of graphs and present a new optimal
    diffusion scheme for general graphs. In the first part of the paper, we introduce
    the Alternating-Direction load balancing scheme, which reduces the number of load
    balance iterations by a factor of 2 for cartesian products of graphs. The resulting
    flow is theoretically analyzed and can be very high for certain cases. Therefore,
    we further present the Mixed-Direction scheme which needs the same number of iterations
    but computes in most cases a much smaller flow. In the second part of the paper,
    we present a simple optimal diffusion scheme for general graphs, calculating a
    balancing flow which is minimal in the l<jats:sub>2</jats:sub> norm. It is based
    on the spectra of the graph representing the network and needs only m-1 iterations
    to balance the load with m being the number of distinct eigenvalues. Known optimal
    diffusion schemes have the same performance, however the optimal scheme presented
    in this paper can be implemented in a very simple manner. The number of iterations
    of optimal diffusion schemes is independent of the load scenario and, thus, they
    are practical for networks which represent graphs with known spectra. Finally,
    our experiments exhibit that the new optimal scheme can successfully be combined
    with the Alternating-Direction and Mixed-Direction schemes for efficient load
    balancing on product graphs. </jats:p>
author:
- first_name: Robert
  full_name: Elsässer, Robert
  last_name: Elsässer
- first_name: Burkhard
  full_name: Monien, Burkhard
  last_name: Monien
- first_name: Robert
  full_name: Preis, Robert
  last_name: Preis
- first_name: Andreas
  full_name: Frommer, Andreas
  last_name: Frommer
citation:
  ama: Elsässer R, Monien B, Preis R, Frommer A. Optimal Diffusion Schemes and Load
    Balancing on Product Graphs. <i>Parallel Processing Letters</i>. 2004:61-73. doi:<a
    href="https://doi.org/10.1142/s0129626404001714">10.1142/s0129626404001714</a>
  apa: Elsässer, R., Monien, B., Preis, R., &#38; Frommer, A. (2004). Optimal Diffusion
    Schemes and Load Balancing on Product Graphs. <i>Parallel Processing Letters</i>,
    61–73. <a href="https://doi.org/10.1142/s0129626404001714">https://doi.org/10.1142/s0129626404001714</a>
  bibtex: '@article{Elsässer_Monien_Preis_Frommer_2004, title={Optimal Diffusion Schemes
    and Load Balancing on Product Graphs}, DOI={<a href="https://doi.org/10.1142/s0129626404001714">10.1142/s0129626404001714</a>},
    journal={Parallel Processing Letters}, author={Elsässer, Robert and Monien, Burkhard
    and Preis, Robert and Frommer, Andreas}, year={2004}, pages={61–73} }'
  chicago: Elsässer, Robert, Burkhard Monien, Robert Preis, and Andreas Frommer. “Optimal
    Diffusion Schemes and Load Balancing on Product Graphs.” <i>Parallel Processing
    Letters</i>, 2004, 61–73. <a href="https://doi.org/10.1142/s0129626404001714">https://doi.org/10.1142/s0129626404001714</a>.
  ieee: R. Elsässer, B. Monien, R. Preis, and A. Frommer, “Optimal Diffusion Schemes
    and Load Balancing on Product Graphs,” <i>Parallel Processing Letters</i>, pp.
    61–73, 2004.
  mla: Elsässer, Robert, et al. “Optimal Diffusion Schemes and Load Balancing on Product
    Graphs.” <i>Parallel Processing Letters</i>, 2004, pp. 61–73, doi:<a href="https://doi.org/10.1142/s0129626404001714">10.1142/s0129626404001714</a>.
  short: R. Elsässer, B. Monien, R. Preis, A. Frommer, Parallel Processing Letters
    (2004) 61–73.
date_created: 2020-04-16T05:46:56Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1142/s0129626404001714
language:
- iso: eng
page: 61-73
publication: Parallel Processing Letters
publication_identifier:
  issn:
  - 0129-6264
  - 1793-642X
publication_status: published
status: public
title: Optimal Diffusion Schemes and Load Balancing on Product Graphs
type: journal_article
user_id: '15701'
year: '2004'
...
---
_id: '16619'
author:
- first_name: Oliver
  full_name: Junge, Oliver
  last_name: Junge
- first_name: Hinke M.
  full_name: Osinga, Hinke M.
  last_name: Osinga
citation:
  ama: 'Junge O, Osinga HM. A set oriented approach to global optimal control. <i>ESAIM:
    Control, Optimisation and Calculus of Variations</i>. 2004:259-270. doi:<a href="https://doi.org/10.1051/cocv:2004006">10.1051/cocv:2004006</a>'
  apa: 'Junge, O., &#38; Osinga, H. M. (2004). A set oriented approach to global optimal
    control. <i>ESAIM: Control, Optimisation and Calculus of Variations</i>, 259–270.
    <a href="https://doi.org/10.1051/cocv:2004006">https://doi.org/10.1051/cocv:2004006</a>'
  bibtex: '@article{Junge_Osinga_2004, title={A set oriented approach to global optimal
    control}, DOI={<a href="https://doi.org/10.1051/cocv:2004006">10.1051/cocv:2004006</a>},
    journal={ESAIM: Control, Optimisation and Calculus of Variations}, author={Junge,
    Oliver and Osinga, Hinke M.}, year={2004}, pages={259–270} }'
  chicago: 'Junge, Oliver, and Hinke M. Osinga. “A Set Oriented Approach to Global
    Optimal Control.” <i>ESAIM: Control, Optimisation and Calculus of Variations</i>,
    2004, 259–70. <a href="https://doi.org/10.1051/cocv:2004006">https://doi.org/10.1051/cocv:2004006</a>.'
  ieee: 'O. Junge and H. M. Osinga, “A set oriented approach to global optimal control,”
    <i>ESAIM: Control, Optimisation and Calculus of Variations</i>, pp. 259–270, 2004.'
  mla: 'Junge, Oliver, and Hinke M. Osinga. “A Set Oriented Approach to Global Optimal
    Control.” <i>ESAIM: Control, Optimisation and Calculus of Variations</i>, 2004,
    pp. 259–70, doi:<a href="https://doi.org/10.1051/cocv:2004006">10.1051/cocv:2004006</a>.'
  short: 'O. Junge, H.M. Osinga, ESAIM: Control, Optimisation and Calculus of Variations
    (2004) 259–270.'
date_created: 2020-04-16T08:11:16Z
date_updated: 2022-01-06T06:52:53Z
department:
- _id: '101'
doi: 10.1051/cocv:2004006
page: 259-270
publication: 'ESAIM: Control, Optimisation and Calculus of Variations'
publication_identifier:
  issn:
  - 1292-8119
  - 1262-3377
publication_status: published
status: public
title: A set oriented approach to global optimal control
type: journal_article
user_id: '15701'
year: '2004'
...
---
_id: '16620'
author:
- first_name: O.
  full_name: Junge, O.
  last_name: Junge
- first_name: J.E.
  full_name: Marsden, J.E.
  last_name: Marsden
- first_name: I.
  full_name: Mezic, I.
  last_name: Mezic
citation:
  ama: 'Junge O, Marsden JE, Mezic I. Uncertainty in the dynamics of conservative
    maps. In: <i>2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat.
    No.04CH37601)</i>. ; 2004. doi:<a href="https://doi.org/10.1109/cdc.2004.1430379">10.1109/cdc.2004.1430379</a>'
  apa: Junge, O., Marsden, J. E., &#38; Mezic, I. (2004). Uncertainty in the dynamics
    of conservative maps. In <i>2004 43rd IEEE Conference on Decision and Control
    (CDC) (IEEE Cat. No.04CH37601)</i>. <a href="https://doi.org/10.1109/cdc.2004.1430379">https://doi.org/10.1109/cdc.2004.1430379</a>
  bibtex: '@inproceedings{Junge_Marsden_Mezic_2004, title={Uncertainty in the dynamics
    of conservative maps}, DOI={<a href="https://doi.org/10.1109/cdc.2004.1430379">10.1109/cdc.2004.1430379</a>},
    booktitle={2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat.
    No.04CH37601)}, author={Junge, O. and Marsden, J.E. and Mezic, I.}, year={2004}
    }'
  chicago: Junge, O., J.E. Marsden, and I. Mezic. “Uncertainty in the Dynamics of
    Conservative Maps.” In <i>2004 43rd IEEE Conference on Decision and Control (CDC)
    (IEEE Cat. No.04CH37601)</i>, 2004. <a href="https://doi.org/10.1109/cdc.2004.1430379">https://doi.org/10.1109/cdc.2004.1430379</a>.
  ieee: O. Junge, J. E. Marsden, and I. Mezic, “Uncertainty in the dynamics of conservative
    maps,” in <i>2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat.
    No.04CH37601)</i>, 2004.
  mla: Junge, O., et al. “Uncertainty in the Dynamics of Conservative Maps.” <i>2004
    43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)</i>,
    2004, doi:<a href="https://doi.org/10.1109/cdc.2004.1430379">10.1109/cdc.2004.1430379</a>.
  short: 'O. Junge, J.E. Marsden, I. Mezic, in: 2004 43rd IEEE Conference on Decision
    and Control (CDC) (IEEE Cat. No.04CH37601), 2004.'
date_created: 2020-04-16T08:12:31Z
date_updated: 2022-01-06T06:52:53Z
department:
- _id: '101'
doi: 10.1109/cdc.2004.1430379
language:
- iso: eng
publication: 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)
publication_identifier:
  isbn:
  - '0780386825'
publication_status: published
status: public
title: Uncertainty in the dynamics of conservative maps
type: conference
user_id: '15701'
year: '2004'
...
---
_id: '16498'
author:
- first_name: P. J.
  full_name: Aston, P. J.
  last_name: Aston
- first_name: M.
  full_name: Dellnitz, M.
  last_name: Dellnitz
citation:
  ama: 'Aston PJ, Dellnitz M. Computation of the dominant Lyapunov exponent via spatial
    integration using matrix norms. <i>Proceedings of the Royal Society of London
    Series A: Mathematical, Physical and Engineering Sciences</i>. 2003:2933-2955.
    doi:<a href="https://doi.org/10.1098/rspa.2003.1143">10.1098/rspa.2003.1143</a>'
  apa: 'Aston, P. J., &#38; Dellnitz, M. (2003). Computation of the dominant Lyapunov
    exponent via spatial integration using matrix norms. <i>Proceedings of the Royal
    Society of London. Series A: Mathematical, Physical and Engineering Sciences</i>,
    2933–2955. <a href="https://doi.org/10.1098/rspa.2003.1143">https://doi.org/10.1098/rspa.2003.1143</a>'
  bibtex: '@article{Aston_Dellnitz_2003, title={Computation of the dominant Lyapunov
    exponent via spatial integration using matrix norms}, DOI={<a href="https://doi.org/10.1098/rspa.2003.1143">10.1098/rspa.2003.1143</a>},
    journal={Proceedings of the Royal Society of London. Series A: Mathematical, Physical
    and Engineering Sciences}, author={Aston, P. J. and Dellnitz, M.}, year={2003},
    pages={2933–2955} }'
  chicago: 'Aston, P. J., and M. Dellnitz. “Computation of the Dominant Lyapunov Exponent
    via Spatial Integration Using Matrix Norms.” <i>Proceedings of the Royal Society
    of London. Series A: Mathematical, Physical and Engineering Sciences</i>, 2003,
    2933–55. <a href="https://doi.org/10.1098/rspa.2003.1143">https://doi.org/10.1098/rspa.2003.1143</a>.'
  ieee: 'P. J. Aston and M. Dellnitz, “Computation of the dominant Lyapunov exponent
    via spatial integration using matrix norms,” <i>Proceedings of the Royal Society
    of London. Series A: Mathematical, Physical and Engineering Sciences</i>, pp.
    2933–2955, 2003.'
  mla: 'Aston, P. J., and M. Dellnitz. “Computation of the Dominant Lyapunov Exponent
    via Spatial Integration Using Matrix Norms.” <i>Proceedings of the Royal Society
    of London. Series A: Mathematical, Physical and Engineering Sciences</i>, 2003,
    pp. 2933–55, doi:<a href="https://doi.org/10.1098/rspa.2003.1143">10.1098/rspa.2003.1143</a>.'
  short: 'P.J. Aston, M. Dellnitz, Proceedings of the Royal Society of London. Series
    A: Mathematical, Physical and Engineering Sciences (2003) 2933–2955.'
date_created: 2020-04-14T09:57:39Z
date_updated: 2022-01-06T06:52:51Z
department:
- _id: '101'
doi: 10.1098/rspa.2003.1143
language:
- iso: eng
page: 2933-2955
publication: 'Proceedings of the Royal Society of London. Series A: Mathematical,
  Physical and Engineering Sciences'
publication_identifier:
  issn:
  - 1364-5021
  - 1471-2946
publication_status: published
status: public
title: Computation of the dominant Lyapunov exponent via spatial integration using
  matrix norms
type: journal_article
user_id: '47427'
year: '2003'
...
---
_id: '16543'
author:
- first_name: Michael
  full_name: Dellnitz, Michael
  last_name: Dellnitz
- first_name: Robert
  full_name: Preis, Robert
  last_name: Preis
citation:
  ama: 'Dellnitz M, Preis R. Congestion and Almost Invariant Sets in Dynamical Systems.
    In: <i>Lecture Notes in Computer Science</i>. Berlin, Heidelberg; 2003. doi:<a
    href="https://doi.org/10.1007/3-540-45084-x_8">10.1007/3-540-45084-x_8</a>'
  apa: Dellnitz, M., &#38; Preis, R. (2003). Congestion and Almost Invariant Sets
    in Dynamical Systems. In <i>Lecture Notes in Computer Science</i>. Berlin, Heidelberg.
    <a href="https://doi.org/10.1007/3-540-45084-x_8">https://doi.org/10.1007/3-540-45084-x_8</a>
  bibtex: '@inbook{Dellnitz_Preis_2003, place={Berlin, Heidelberg}, title={Congestion
    and Almost Invariant Sets in Dynamical Systems}, DOI={<a href="https://doi.org/10.1007/3-540-45084-x_8">10.1007/3-540-45084-x_8</a>},
    booktitle={Lecture Notes in Computer Science}, author={Dellnitz, Michael and Preis,
    Robert}, year={2003} }'
  chicago: Dellnitz, Michael, and Robert Preis. “Congestion and Almost Invariant Sets
    in Dynamical Systems.” In <i>Lecture Notes in Computer Science</i>. Berlin, Heidelberg,
    2003. <a href="https://doi.org/10.1007/3-540-45084-x_8">https://doi.org/10.1007/3-540-45084-x_8</a>.
  ieee: M. Dellnitz and R. Preis, “Congestion and Almost Invariant Sets in Dynamical
    Systems,” in <i>Lecture Notes in Computer Science</i>, Berlin, Heidelberg, 2003.
  mla: Dellnitz, Michael, and Robert Preis. “Congestion and Almost Invariant Sets
    in Dynamical Systems.” <i>Lecture Notes in Computer Science</i>, 2003, doi:<a
    href="https://doi.org/10.1007/3-540-45084-x_8">10.1007/3-540-45084-x_8</a>.
  short: 'M. Dellnitz, R. Preis, in: Lecture Notes in Computer Science, Berlin, Heidelberg,
    2003.'
date_created: 2020-04-15T08:50:07Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1007/3-540-45084-x_8
language:
- iso: eng
place: Berlin, Heidelberg
publication: Lecture Notes in Computer Science
publication_identifier:
  isbn:
  - '9783540405542'
  - '9783540450849'
  issn:
  - 0302-9743
publication_status: published
status: public
title: Congestion and Almost Invariant Sets in Dynamical Systems
type: book_chapter
user_id: '15701'
year: '2003'
...
---
_id: '16600'
author:
- first_name: Gary
  full_name: Froyland, Gary
  last_name: Froyland
- first_name: Michael
  full_name: Dellnitz, Michael
  last_name: Dellnitz
citation:
  ama: Froyland G, Dellnitz M. Detecting and Locating Near-Optimal Almost-Invariant
    Sets and Cycles. <i>SIAM Journal on Scientific Computing</i>. 2003:1839-1863.
    doi:<a href="https://doi.org/10.1137/s106482750238911x">10.1137/s106482750238911x</a>
  apa: Froyland, G., &#38; Dellnitz, M. (2003). Detecting and Locating Near-Optimal
    Almost-Invariant Sets and Cycles. <i>SIAM Journal on Scientific Computing</i>,
    1839–1863. <a href="https://doi.org/10.1137/s106482750238911x">https://doi.org/10.1137/s106482750238911x</a>
  bibtex: '@article{Froyland_Dellnitz_2003, title={Detecting and Locating Near-Optimal
    Almost-Invariant Sets and Cycles}, DOI={<a href="https://doi.org/10.1137/s106482750238911x">10.1137/s106482750238911x</a>},
    journal={SIAM Journal on Scientific Computing}, author={Froyland, Gary and Dellnitz,
    Michael}, year={2003}, pages={1839–1863} }'
  chicago: Froyland, Gary, and Michael Dellnitz. “Detecting and Locating Near-Optimal
    Almost-Invariant Sets and Cycles.” <i>SIAM Journal on Scientific Computing</i>,
    2003, 1839–63. <a href="https://doi.org/10.1137/s106482750238911x">https://doi.org/10.1137/s106482750238911x</a>.
  ieee: G. Froyland and M. Dellnitz, “Detecting and Locating Near-Optimal Almost-Invariant
    Sets and Cycles,” <i>SIAM Journal on Scientific Computing</i>, pp. 1839–1863,
    2003.
  mla: Froyland, Gary, and Michael Dellnitz. “Detecting and Locating Near-Optimal
    Almost-Invariant Sets and Cycles.” <i>SIAM Journal on Scientific Computing</i>,
    2003, pp. 1839–63, doi:<a href="https://doi.org/10.1137/s106482750238911x">10.1137/s106482750238911x</a>.
  short: G. Froyland, M. Dellnitz, SIAM Journal on Scientific Computing (2003) 1839–1863.
date_created: 2020-04-16T06:07:10Z
date_updated: 2022-01-06T06:52:53Z
department:
- _id: '101'
doi: 10.1137/s106482750238911x
language:
- iso: eng
page: 1839-1863
publication: SIAM Journal on Scientific Computing
publication_identifier:
  issn:
  - 1064-8275
  - 1095-7197
publication_status: published
status: public
title: Detecting and Locating Near-Optimal Almost-Invariant Sets and Cycles
type: journal_article
user_id: '15701'
year: '2003'
...
---
_id: '16664'
author:
- first_name: Oliver
  full_name: Schütze, Oliver
  last_name: Schütze
citation:
  ama: 'Schütze O. A New Data Structure for the Nondominance Problem in Multi-objective
    Optimization. In: <i>Lecture Notes in Computer Science</i>. Berlin, Heidelberg;
    2003. doi:<a href="https://doi.org/10.1007/3-540-36970-8_36">10.1007/3-540-36970-8_36</a>'
  apa: Schütze, O. (2003). A New Data Structure for the Nondominance Problem in Multi-objective
    Optimization. In <i>Lecture Notes in Computer Science</i>. Berlin, Heidelberg.
    <a href="https://doi.org/10.1007/3-540-36970-8_36">https://doi.org/10.1007/3-540-36970-8_36</a>
  bibtex: '@inbook{Schütze_2003, place={Berlin, Heidelberg}, title={A New Data Structure
    for the Nondominance Problem in Multi-objective Optimization}, DOI={<a href="https://doi.org/10.1007/3-540-36970-8_36">10.1007/3-540-36970-8_36</a>},
    booktitle={Lecture Notes in Computer Science}, author={Schütze, Oliver}, year={2003}
    }'
  chicago: Schütze, Oliver. “A New Data Structure for the Nondominance Problem in
    Multi-Objective Optimization.” In <i>Lecture Notes in Computer Science</i>. Berlin,
    Heidelberg, 2003. <a href="https://doi.org/10.1007/3-540-36970-8_36">https://doi.org/10.1007/3-540-36970-8_36</a>.
  ieee: O. Schütze, “A New Data Structure for the Nondominance Problem in Multi-objective
    Optimization,” in <i>Lecture Notes in Computer Science</i>, Berlin, Heidelberg,
    2003.
  mla: Schütze, Oliver. “A New Data Structure for the Nondominance Problem in Multi-Objective
    Optimization.” <i>Lecture Notes in Computer Science</i>, 2003, doi:<a href="https://doi.org/10.1007/3-540-36970-8_36">10.1007/3-540-36970-8_36</a>.
  short: 'O. Schütze, in: Lecture Notes in Computer Science, Berlin, Heidelberg, 2003.'
date_created: 2020-04-16T09:57:05Z
date_updated: 2022-01-06T06:52:54Z
department:
- _id: '101'
doi: 10.1007/3-540-36970-8_36
language:
- iso: eng
place: Berlin, Heidelberg
publication: Lecture Notes in Computer Science
publication_identifier:
  isbn:
  - '9783540018698'
  - '9783540369707'
  issn:
  - 0302-9743
publication_status: published
status: public
title: A New Data Structure for the Nondominance Problem in Multi-objective Optimization
type: book_chapter
user_id: '15701'
year: '2003'
...
---
_id: '16665'
author:
- first_name: Oliver
  full_name: Schütze, Oliver
  last_name: Schütze
- first_name: Sanaz
  full_name: Mostaghim, Sanaz
  last_name: Mostaghim
- first_name: Michael
  full_name: Dellnitz, Michael
  last_name: Dellnitz
- first_name: Jürgen
  full_name: Teich, Jürgen
  last_name: Teich
citation:
  ama: 'Schütze O, Mostaghim S, Dellnitz M, Teich J. Covering Pareto Sets by Multilevel
    Evolutionary Subdivision Techniques. In: <i>Lecture Notes in Computer Science</i>.
    Berlin, Heidelberg; 2003. doi:<a href="https://doi.org/10.1007/3-540-36970-8_9">10.1007/3-540-36970-8_9</a>'
  apa: Schütze, O., Mostaghim, S., Dellnitz, M., &#38; Teich, J. (2003). Covering
    Pareto Sets by Multilevel Evolutionary Subdivision Techniques. In <i>Lecture Notes
    in Computer Science</i>. Berlin, Heidelberg. <a href="https://doi.org/10.1007/3-540-36970-8_9">https://doi.org/10.1007/3-540-36970-8_9</a>
  bibtex: '@inbook{Schütze_Mostaghim_Dellnitz_Teich_2003, place={Berlin, Heidelberg},
    title={Covering Pareto Sets by Multilevel Evolutionary Subdivision Techniques},
    DOI={<a href="https://doi.org/10.1007/3-540-36970-8_9">10.1007/3-540-36970-8_9</a>},
    booktitle={Lecture Notes in Computer Science}, author={Schütze, Oliver and Mostaghim,
    Sanaz and Dellnitz, Michael and Teich, Jürgen}, year={2003} }'
  chicago: Schütze, Oliver, Sanaz Mostaghim, Michael Dellnitz, and Jürgen Teich. “Covering
    Pareto Sets by Multilevel Evolutionary Subdivision Techniques.” In <i>Lecture
    Notes in Computer Science</i>. Berlin, Heidelberg, 2003. <a href="https://doi.org/10.1007/3-540-36970-8_9">https://doi.org/10.1007/3-540-36970-8_9</a>.
  ieee: O. Schütze, S. Mostaghim, M. Dellnitz, and J. Teich, “Covering Pareto Sets
    by Multilevel Evolutionary Subdivision Techniques,” in <i>Lecture Notes in Computer
    Science</i>, Berlin, Heidelberg, 2003.
  mla: Schütze, Oliver, et al. “Covering Pareto Sets by Multilevel Evolutionary Subdivision
    Techniques.” <i>Lecture Notes in Computer Science</i>, 2003, doi:<a href="https://doi.org/10.1007/3-540-36970-8_9">10.1007/3-540-36970-8_9</a>.
  short: 'O. Schütze, S. Mostaghim, M. Dellnitz, J. Teich, in: Lecture Notes in Computer
    Science, Berlin, Heidelberg, 2003.'
date_created: 2020-04-16T09:58:10Z
date_updated: 2022-01-06T06:52:54Z
department:
- _id: '101'
doi: 10.1007/3-540-36970-8_9
language:
- iso: eng
place: Berlin, Heidelberg
publication: Lecture Notes in Computer Science
publication_identifier:
  isbn:
  - '9783540018698'
  - '9783540369707'
  issn:
  - 0302-9743
publication_status: published
status: public
title: Covering Pareto Sets by Multilevel Evolutionary Subdivision Techniques
type: book_chapter
user_id: '15701'
year: '2003'
...
---
_id: '34896'
abstract:
- lang: eng
  text: We apply class field theory to the computation of the minimal discriminants
    for certain solvable groups. In particular, we apply our techniques to small Frobenius
    groups and all imprimitive degree 8 groups such that the corresponding fields
    have only a degree 2 and no degree 4 subfield.
author:
- first_name: Claus
  full_name: Fieker, Claus
  last_name: Fieker
- first_name: Jürgen
  full_name: Klüners, Jürgen
  id: '21202'
  last_name: Klüners
citation:
  ama: Fieker C, Klüners J. Minimal discriminants for fields with small Frobenius
    groups as Galois groups. <i>Journal of Number Theory</i>. 2003;99(2):318-337.
    doi:<a href="https://doi.org/10.1016/s0022-314x(02)00071-9">10.1016/s0022-314x(02)00071-9</a>
  apa: Fieker, C., &#38; Klüners, J. (2003). Minimal discriminants for fields with
    small Frobenius groups as Galois groups. <i>Journal of Number Theory</i>, <i>99</i>(2),
    318–337. <a href="https://doi.org/10.1016/s0022-314x(02)00071-9">https://doi.org/10.1016/s0022-314x(02)00071-9</a>
  bibtex: '@article{Fieker_Klüners_2003, title={Minimal discriminants for fields with
    small Frobenius groups as Galois groups}, volume={99}, DOI={<a href="https://doi.org/10.1016/s0022-314x(02)00071-9">10.1016/s0022-314x(02)00071-9</a>},
    number={2}, journal={Journal of Number Theory}, publisher={Elsevier BV}, author={Fieker,
    Claus and Klüners, Jürgen}, year={2003}, pages={318–337} }'
  chicago: 'Fieker, Claus, and Jürgen Klüners. “Minimal Discriminants for Fields with
    Small Frobenius Groups as Galois Groups.” <i>Journal of Number Theory</i> 99,
    no. 2 (2003): 318–37. <a href="https://doi.org/10.1016/s0022-314x(02)00071-9">https://doi.org/10.1016/s0022-314x(02)00071-9</a>.'
  ieee: 'C. Fieker and J. Klüners, “Minimal discriminants for fields with small Frobenius
    groups as Galois groups,” <i>Journal of Number Theory</i>, vol. 99, no. 2, pp.
    318–337, 2003, doi: <a href="https://doi.org/10.1016/s0022-314x(02)00071-9">10.1016/s0022-314x(02)00071-9</a>.'
  mla: Fieker, Claus, and Jürgen Klüners. “Minimal Discriminants for Fields with Small
    Frobenius Groups as Galois Groups.” <i>Journal of Number Theory</i>, vol. 99,
    no. 2, Elsevier BV, 2003, pp. 318–37, doi:<a href="https://doi.org/10.1016/s0022-314x(02)00071-9">10.1016/s0022-314x(02)00071-9</a>.
  short: C. Fieker, J. Klüners, Journal of Number Theory 99 (2003) 318–337.
date_created: 2022-12-23T09:53:23Z
date_updated: 2023-03-06T09:19:16Z
department:
- _id: '102'
doi: 10.1016/s0022-314x(02)00071-9
intvolume: '        99'
issue: '2'
keyword:
- Algebra and Number Theory
language:
- iso: eng
page: 318-337
publication: Journal of Number Theory
publication_identifier:
  issn:
  - 0022-314X
publication_status: published
publisher: Elsevier BV
status: public
title: Minimal discriminants for fields with small Frobenius groups as Galois groups
type: journal_article
user_id: '93826'
volume: 99
year: '2003'
...
---
_id: '16538'
author:
- first_name: Michael
  full_name: Dellnitz, Michael
  last_name: Dellnitz
- first_name: Oliver
  full_name: Junge, Oliver
  last_name: Junge
citation:
  ama: 'Dellnitz M, Junge O. Set Oriented Numerical Methods for Dynamical Systems.
    In: <i>Handbook of Dynamical Systems</i>. ; 2002. doi:<a href="https://doi.org/10.1016/s1874-575x(02)80026-1">10.1016/s1874-575x(02)80026-1</a>'
  apa: Dellnitz, M., &#38; Junge, O. (2002). Set Oriented Numerical Methods for Dynamical
    Systems. In <i>Handbook of Dynamical Systems</i>. <a href="https://doi.org/10.1016/s1874-575x(02)80026-1">https://doi.org/10.1016/s1874-575x(02)80026-1</a>
  bibtex: '@inbook{Dellnitz_Junge_2002, title={Set Oriented Numerical Methods for
    Dynamical Systems}, DOI={<a href="https://doi.org/10.1016/s1874-575x(02)80026-1">10.1016/s1874-575x(02)80026-1</a>},
    booktitle={Handbook of Dynamical Systems}, author={Dellnitz, Michael and Junge,
    Oliver}, year={2002} }'
  chicago: Dellnitz, Michael, and Oliver Junge. “Set Oriented Numerical Methods for
    Dynamical Systems.” In <i>Handbook of Dynamical Systems</i>, 2002. <a href="https://doi.org/10.1016/s1874-575x(02)80026-1">https://doi.org/10.1016/s1874-575x(02)80026-1</a>.
  ieee: M. Dellnitz and O. Junge, “Set Oriented Numerical Methods for Dynamical Systems,”
    in <i>Handbook of Dynamical Systems</i>, 2002.
  mla: Dellnitz, Michael, and Oliver Junge. “Set Oriented Numerical Methods for Dynamical
    Systems.” <i>Handbook of Dynamical Systems</i>, 2002, doi:<a href="https://doi.org/10.1016/s1874-575x(02)80026-1">10.1016/s1874-575x(02)80026-1</a>.
  short: 'M. Dellnitz, O. Junge, in: Handbook of Dynamical Systems, 2002.'
date_created: 2020-04-15T08:37:59Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1016/s1874-575x(02)80026-1
language:
- iso: eng
publication: Handbook of Dynamical Systems
publication_identifier:
  isbn:
  - '9780444501684'
  issn:
  - 1874-575X
publication_status: published
status: public
title: Set Oriented Numerical Methods for Dynamical Systems
type: book_chapter
user_id: '15701'
year: '2002'
...
---
_id: '16556'
author:
- first_name: M.
  full_name: Dellnitz, M.
  last_name: Dellnitz
citation:
  ama: Dellnitz M. Finding zeros by multilevel subdivision techniques. <i>IMA Journal
    of Numerical Analysis</i>. 2002:167-185. doi:<a href="https://doi.org/10.1093/imanum/22.2.167">10.1093/imanum/22.2.167</a>
  apa: Dellnitz, M. (2002). Finding zeros by multilevel subdivision techniques. <i>IMA
    Journal of Numerical Analysis</i>, 167–185. <a href="https://doi.org/10.1093/imanum/22.2.167">https://doi.org/10.1093/imanum/22.2.167</a>
  bibtex: '@article{Dellnitz_2002, title={Finding zeros by multilevel subdivision
    techniques}, DOI={<a href="https://doi.org/10.1093/imanum/22.2.167">10.1093/imanum/22.2.167</a>},
    journal={IMA Journal of Numerical Analysis}, author={Dellnitz, M.}, year={2002},
    pages={167–185} }'
  chicago: Dellnitz, M. “Finding Zeros by Multilevel Subdivision Techniques.” <i>IMA
    Journal of Numerical Analysis</i>, 2002, 167–85. <a href="https://doi.org/10.1093/imanum/22.2.167">https://doi.org/10.1093/imanum/22.2.167</a>.
  ieee: M. Dellnitz, “Finding zeros by multilevel subdivision techniques,” <i>IMA
    Journal of Numerical Analysis</i>, pp. 167–185, 2002.
  mla: Dellnitz, M. “Finding Zeros by Multilevel Subdivision Techniques.” <i>IMA Journal
    of Numerical Analysis</i>, 2002, pp. 167–85, doi:<a href="https://doi.org/10.1093/imanum/22.2.167">10.1093/imanum/22.2.167</a>.
  short: M. Dellnitz, IMA Journal of Numerical Analysis (2002) 167–185.
date_created: 2020-04-15T09:12:17Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1093/imanum/22.2.167
language:
- iso: eng
page: 167-185
publication: IMA Journal of Numerical Analysis
publication_identifier:
  issn:
  - 0272-4979
  - 1464-3642
publication_status: published
status: public
title: Finding zeros by multilevel subdivision techniques
type: journal_article
user_id: '15701'
year: '2002'
...
---
_id: '16586'
author:
- first_name: Robert
  full_name: Elsässer, Robert
  last_name: Elsässer
- first_name: Burkhard
  full_name: Monien, Burkhard
  last_name: Monien
- first_name: Robert
  full_name: Preis, Robert
  last_name: Preis
citation:
  ama: Elsässer R, Monien B, Preis R. Diffusion Schemes for Load Balancing on Heterogeneous
    Networks. <i>Theory of Computing Systems</i>. 2002:305-320. doi:<a href="https://doi.org/10.1007/s00224-002-1056-4">10.1007/s00224-002-1056-4</a>
  apa: Elsässer, R., Monien, B., &#38; Preis, R. (2002). Diffusion Schemes for Load
    Balancing on Heterogeneous Networks. <i>Theory of Computing Systems</i>, 305–320.
    <a href="https://doi.org/10.1007/s00224-002-1056-4">https://doi.org/10.1007/s00224-002-1056-4</a>
  bibtex: '@article{Elsässer_Monien_Preis_2002, title={Diffusion Schemes for Load
    Balancing on Heterogeneous Networks}, DOI={<a href="https://doi.org/10.1007/s00224-002-1056-4">10.1007/s00224-002-1056-4</a>},
    journal={Theory of Computing Systems}, author={Elsässer, Robert and Monien, Burkhard
    and Preis, Robert}, year={2002}, pages={305–320} }'
  chicago: Elsässer, Robert, Burkhard Monien, and Robert Preis. “Diffusion Schemes
    for Load Balancing on Heterogeneous Networks.” <i>Theory of Computing Systems</i>,
    2002, 305–20. <a href="https://doi.org/10.1007/s00224-002-1056-4">https://doi.org/10.1007/s00224-002-1056-4</a>.
  ieee: R. Elsässer, B. Monien, and R. Preis, “Diffusion Schemes for Load Balancing
    on Heterogeneous Networks,” <i>Theory of Computing Systems</i>, pp. 305–320, 2002.
  mla: Elsässer, Robert, et al. “Diffusion Schemes for Load Balancing on Heterogeneous
    Networks.” <i>Theory of Computing Systems</i>, 2002, pp. 305–20, doi:<a href="https://doi.org/10.1007/s00224-002-1056-4">10.1007/s00224-002-1056-4</a>.
  short: R. Elsässer, B. Monien, R. Preis, Theory of Computing Systems (2002) 305–320.
date_created: 2020-04-16T05:45:42Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1007/s00224-002-1056-4
language:
- iso: eng
page: 305-320
publication: Theory of Computing Systems
publication_identifier:
  issn:
  - 1432-4350
  - 1433-0490
publication_status: published
status: public
title: Diffusion Schemes for Load Balancing on Heterogeneous Networks
type: journal_article
user_id: '15701'
year: '2002'
...
---
_id: '35954'
abstract:
- lang: eng
  text: 'Let {\ASIE K}\,/{\small \ℚ}({\ASIE t \!}) be a finite extension. We describe
    algorithms for computing subfields and automorphisms of {\ASIE K}\,/{\small \ℚ}({\ASIE
    t }\!). As an application we give an algorithm for finding decompositions of rational
    functions in {\small \ℚ(α)}. We also present an algorithm which decides if an
    extension {\ASIE L}\,/{\small \ℚ}({\ASIE t \!}) is a subfield of {\ASIE K}. In
    case [{\ASIE K : \;}{\small\ℚ}({\ASIE t \!})] = [{\ASIE L : \;}{\small \ℚ}({\ASIE
    t \!})] we obtain a {\small \ℚ}({\ASIE t \!})-isomorphism test. Furthermore, we
    describe an algorithm which computes subfields of the normal closure of {\ASIE
    K}\,/{\small \ℚ}({\ASIE t \!}).'
author:
- first_name: Jürgen
  full_name: Klüners, Jürgen
  id: '21202'
  last_name: Klüners
citation:
  ama: Klüners J. Algorithms for function fields. <i>Experiment Math </i>. 2002;11(2):171-181.
  apa: Klüners, J. (2002). Algorithms for function fields. <i>Experiment. Math. </i>,
    <i>11</i>(2), 171–181.
  bibtex: '@article{Klüners_2002, title={Algorithms for function fields}, volume={11},
    number={2}, journal={Experiment. Math. }, publisher={Elsevier BV}, author={Klüners,
    Jürgen}, year={2002}, pages={171–181} }'
  chicago: 'Klüners, Jürgen. “Algorithms for Function Fields.” <i>Experiment. Math.
    </i> 11, no. 2 (2002): 171–81.'
  ieee: J. Klüners, “Algorithms for function fields,” <i>Experiment. Math. </i>, vol.
    11, no. 2, pp. 171–181, 2002.
  mla: Klüners, Jürgen. “Algorithms for Function Fields.” <i>Experiment. Math. </i>,
    vol. 11, no. 2, Elsevier BV, 2002, pp. 171–81.
  short: J. Klüners, Experiment. Math.  11 (2002) 171–181.
date_created: 2023-01-11T09:45:40Z
date_updated: 2023-03-06T10:26:58Z
department:
- _id: '102'
intvolume: '        11'
issue: '2'
keyword:
- algorithms
- decompositions
- Galois groups
- subfields
language:
- iso: eng
page: 171-181
publication: 'Experiment. Math. '
publication_status: published
publisher: Elsevier BV
related_material:
  link:
  - relation: confirmation
    url: https://projecteuclid.org/journals/experimental-mathematics/volume-11/issue-2/Algorithms-for-function-fields/em/1062621213.full
status: public
title: Algorithms for function fields
type: journal_article
user_id: '93826'
volume: 11
year: '2002'
...
---
_id: '16555'
author:
- first_name: Michael
  full_name: Dellnitz, Michael
  last_name: Dellnitz
- first_name: Gary
  full_name: Froyland, Gary
  last_name: Froyland
- first_name: Oliver
  full_name: Junge, Oliver
  last_name: Junge
citation:
  ama: 'Dellnitz M, Froyland G, Junge O. The Algorithms Behind GAIO — Set Oriented
    Numerical Methods for Dynamical Systems. In: <i>Ergodic Theory, Analysis, and
    Efficient Simulation of Dynamical Systems</i>. Berlin, Heidelberg; 2001. doi:<a
    href="https://doi.org/10.1007/978-3-642-56589-2_7">10.1007/978-3-642-56589-2_7</a>'
  apa: Dellnitz, M., Froyland, G., &#38; Junge, O. (2001). The Algorithms Behind GAIO
    — Set Oriented Numerical Methods for Dynamical Systems. In <i>Ergodic Theory,
    Analysis, and Efficient Simulation of Dynamical Systems</i>. Berlin, Heidelberg.
    <a href="https://doi.org/10.1007/978-3-642-56589-2_7">https://doi.org/10.1007/978-3-642-56589-2_7</a>
  bibtex: '@inbook{Dellnitz_Froyland_Junge_2001, place={Berlin, Heidelberg}, title={The
    Algorithms Behind GAIO — Set Oriented Numerical Methods for Dynamical Systems},
    DOI={<a href="https://doi.org/10.1007/978-3-642-56589-2_7">10.1007/978-3-642-56589-2_7</a>},
    booktitle={Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems},
    author={Dellnitz, Michael and Froyland, Gary and Junge, Oliver}, year={2001} }'
  chicago: Dellnitz, Michael, Gary Froyland, and Oliver Junge. “The Algorithms Behind
    GAIO — Set Oriented Numerical Methods for Dynamical Systems.” In <i>Ergodic Theory,
    Analysis, and Efficient Simulation of Dynamical Systems</i>. Berlin, Heidelberg,
    2001. <a href="https://doi.org/10.1007/978-3-642-56589-2_7">https://doi.org/10.1007/978-3-642-56589-2_7</a>.
  ieee: M. Dellnitz, G. Froyland, and O. Junge, “The Algorithms Behind GAIO — Set
    Oriented Numerical Methods for Dynamical Systems,” in <i>Ergodic Theory, Analysis,
    and Efficient Simulation of Dynamical Systems</i>, Berlin, Heidelberg, 2001.
  mla: Dellnitz, Michael, et al. “The Algorithms Behind GAIO — Set Oriented Numerical
    Methods for Dynamical Systems.” <i>Ergodic Theory, Analysis, and Efficient Simulation
    of Dynamical Systems</i>, 2001, doi:<a href="https://doi.org/10.1007/978-3-642-56589-2_7">10.1007/978-3-642-56589-2_7</a>.
  short: 'M. Dellnitz, G. Froyland, O. Junge, in: Ergodic Theory, Analysis, and Efficient
    Simulation of Dynamical Systems, Berlin, Heidelberg, 2001.'
date_created: 2020-04-15T09:10:54Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1007/978-3-642-56589-2_7
language:
- iso: eng
place: Berlin, Heidelberg
publication: Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems
publication_identifier:
  isbn:
  - '9783642625244'
  - '9783642565892'
publication_status: published
status: public
title: The Algorithms Behind GAIO — Set Oriented Numerical Methods for Dynamical Systems
type: book_chapter
user_id: '15701'
year: '2001'
...
---
_id: '16598'
author:
- first_name: Gary
  full_name: Froyland, Gary
  last_name: Froyland
citation:
  ama: 'Froyland G. Extracting Dynamical Behavior via Markov Models. In: <i>Nonlinear
    Dynamics and Statistics</i>. Boston, MA; 2001. doi:<a href="https://doi.org/10.1007/978-1-4612-0177-9_12">10.1007/978-1-4612-0177-9_12</a>'
  apa: Froyland, G. (2001). Extracting Dynamical Behavior via Markov Models. In <i>Nonlinear
    Dynamics and Statistics</i>. Boston, MA. <a href="https://doi.org/10.1007/978-1-4612-0177-9_12">https://doi.org/10.1007/978-1-4612-0177-9_12</a>
  bibtex: '@inbook{Froyland_2001, place={Boston, MA}, title={Extracting Dynamical
    Behavior via Markov Models}, DOI={<a href="https://doi.org/10.1007/978-1-4612-0177-9_12">10.1007/978-1-4612-0177-9_12</a>},
    booktitle={Nonlinear Dynamics and Statistics}, author={Froyland, Gary}, year={2001}
    }'
  chicago: Froyland, Gary. “Extracting Dynamical Behavior via Markov Models.” In <i>Nonlinear
    Dynamics and Statistics</i>. Boston, MA, 2001. <a href="https://doi.org/10.1007/978-1-4612-0177-9_12">https://doi.org/10.1007/978-1-4612-0177-9_12</a>.
  ieee: G. Froyland, “Extracting Dynamical Behavior via Markov Models,” in <i>Nonlinear
    Dynamics and Statistics</i>, Boston, MA, 2001.
  mla: Froyland, Gary. “Extracting Dynamical Behavior via Markov Models.” <i>Nonlinear
    Dynamics and Statistics</i>, 2001, doi:<a href="https://doi.org/10.1007/978-1-4612-0177-9_12">10.1007/978-1-4612-0177-9_12</a>.
  short: 'G. Froyland, in: Nonlinear Dynamics and Statistics, Boston, MA, 2001.'
date_created: 2020-04-16T06:03:45Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1007/978-1-4612-0177-9_12
language:
- iso: eng
place: Boston, MA
publication: Nonlinear Dynamics and Statistics
publication_identifier:
  isbn:
  - '9781461266488'
  - '9781461201779'
publication_status: published
status: public
title: Extracting Dynamical Behavior via Markov Models
type: book_chapter
user_id: '15701'
year: '2001'
...
---
_id: '16601'
author:
- first_name: Gary
  full_name: Froyland, Gary
  last_name: Froyland
- first_name: Oliver
  full_name: Junge, Oliver
  last_name: Junge
- first_name: Gunter
  full_name: Ochs, Gunter
  last_name: Ochs
citation:
  ama: 'Froyland G, Junge O, Ochs G. Rigorous computation of topological entropy with
    respect to a finite partition. <i>Physica D: Nonlinear Phenomena</i>. 2001:68-84.
    doi:<a href="https://doi.org/10.1016/s0167-2789(01)00216-0">10.1016/s0167-2789(01)00216-0</a>'
  apa: 'Froyland, G., Junge, O., &#38; Ochs, G. (2001). Rigorous computation of topological
    entropy with respect to a finite partition. <i>Physica D: Nonlinear Phenomena</i>,
    68–84. <a href="https://doi.org/10.1016/s0167-2789(01)00216-0">https://doi.org/10.1016/s0167-2789(01)00216-0</a>'
  bibtex: '@article{Froyland_Junge_Ochs_2001, title={Rigorous computation of topological
    entropy with respect to a finite partition}, DOI={<a href="https://doi.org/10.1016/s0167-2789(01)00216-0">10.1016/s0167-2789(01)00216-0</a>},
    journal={Physica D: Nonlinear Phenomena}, author={Froyland, Gary and Junge, Oliver
    and Ochs, Gunter}, year={2001}, pages={68–84} }'
  chicago: 'Froyland, Gary, Oliver Junge, and Gunter Ochs. “Rigorous Computation of
    Topological Entropy with Respect to a Finite Partition.” <i>Physica D: Nonlinear
    Phenomena</i>, 2001, 68–84. <a href="https://doi.org/10.1016/s0167-2789(01)00216-0">https://doi.org/10.1016/s0167-2789(01)00216-0</a>.'
  ieee: 'G. Froyland, O. Junge, and G. Ochs, “Rigorous computation of topological
    entropy with respect to a finite partition,” <i>Physica D: Nonlinear Phenomena</i>,
    pp. 68–84, 2001.'
  mla: 'Froyland, Gary, et al. “Rigorous Computation of Topological Entropy with Respect
    to a Finite Partition.” <i>Physica D: Nonlinear Phenomena</i>, 2001, pp. 68–84,
    doi:<a href="https://doi.org/10.1016/s0167-2789(01)00216-0">10.1016/s0167-2789(01)00216-0</a>.'
  short: 'G. Froyland, O. Junge, G. Ochs, Physica D: Nonlinear Phenomena (2001) 68–84.'
date_created: 2020-04-16T06:08:12Z
date_updated: 2022-01-06T06:52:53Z
department:
- _id: '101'
doi: 10.1016/s0167-2789(01)00216-0
language:
- iso: eng
page: 68-84
publication: 'Physica D: Nonlinear Phenomena'
publication_identifier:
  issn:
  - 0167-2789
publication_status: published
status: public
title: Rigorous computation of topological entropy with respect to a finite partition
type: journal_article
user_id: '15701'
year: '2001'
...
---
_id: '16617'
author:
- first_name: Oliver
  full_name: Junge, Oliver
  last_name: Junge
citation:
  ama: 'Junge O. An adaptive subdivision technique for the approximation of attractors
    and invariant measures: proof of convergence. <i>Dynamical Systems</i>. 2001:213-222.
    doi:<a href="https://doi.org/10.1080/14689360109696233">10.1080/14689360109696233</a>'
  apa: 'Junge, O. (2001). An adaptive subdivision technique for the approximation
    of attractors and invariant measures: proof of convergence. <i>Dynamical Systems</i>,
    213–222. <a href="https://doi.org/10.1080/14689360109696233">https://doi.org/10.1080/14689360109696233</a>'
  bibtex: '@article{Junge_2001, title={An adaptive subdivision technique for the approximation
    of attractors and invariant measures: proof of convergence}, DOI={<a href="https://doi.org/10.1080/14689360109696233">10.1080/14689360109696233</a>},
    journal={Dynamical Systems}, author={Junge, Oliver}, year={2001}, pages={213–222}
    }'
  chicago: 'Junge, Oliver. “An Adaptive Subdivision Technique for the Approximation
    of Attractors and Invariant Measures: Proof of Convergence.” <i>Dynamical Systems</i>,
    2001, 213–22. <a href="https://doi.org/10.1080/14689360109696233">https://doi.org/10.1080/14689360109696233</a>.'
  ieee: 'O. Junge, “An adaptive subdivision technique for the approximation of attractors
    and invariant measures: proof of convergence,” <i>Dynamical Systems</i>, pp. 213–222,
    2001.'
  mla: 'Junge, Oliver. “An Adaptive Subdivision Technique for the Approximation of
    Attractors and Invariant Measures: Proof of Convergence.” <i>Dynamical Systems</i>,
    2001, pp. 213–22, doi:<a href="https://doi.org/10.1080/14689360109696233">10.1080/14689360109696233</a>.'
  short: O. Junge, Dynamical Systems (2001) 213–222.
date_created: 2020-04-16T08:09:10Z
date_updated: 2022-01-06T06:52:53Z
department:
- _id: '101'
doi: 10.1080/14689360109696233
language:
- iso: eng
page: 213-222
publication: Dynamical Systems
publication_identifier:
  issn:
  - 1468-9367
  - 1468-9375
publication_status: published
status: public
title: 'An adaptive subdivision technique for the approximation of attractors and
  invariant measures: proof of convergence'
type: journal_article
user_id: '15701'
year: '2001'
...
---
_id: '34897'
abstract:
- lang: eng
  text: This paper announces the creation of a database for number fields. It describes
    the contents and the methods of access, indicates the origin of the polynomials,
    and formulates the aims of this collection of fields.
author:
- first_name: Jürgen
  full_name: Klüners, Jürgen
  id: '21202'
  last_name: Klüners
- first_name: Gunter
  full_name: Malle, Gunter
  last_name: Malle
citation:
  ama: Klüners J, Malle G. A Database for Field Extensions of the Rationals. <i>LMS
    Journal of Computation and Mathematics</i>. 2001;4:182-196. doi:<a href="https://doi.org/10.1112/s1461157000000851">10.1112/s1461157000000851</a>
  apa: Klüners, J., &#38; Malle, G. (2001). A Database for Field Extensions of the
    Rationals. <i>LMS Journal of Computation and Mathematics</i>, <i>4</i>, 182–196.
    <a href="https://doi.org/10.1112/s1461157000000851">https://doi.org/10.1112/s1461157000000851</a>
  bibtex: '@article{Klüners_Malle_2001, title={A Database for Field Extensions of
    the Rationals}, volume={4}, DOI={<a href="https://doi.org/10.1112/s1461157000000851">10.1112/s1461157000000851</a>},
    journal={LMS Journal of Computation and Mathematics}, publisher={Wiley}, author={Klüners,
    Jürgen and Malle, Gunter}, year={2001}, pages={182–196} }'
  chicago: 'Klüners, Jürgen, and Gunter Malle. “A Database for Field Extensions of
    the Rationals.” <i>LMS Journal of Computation and Mathematics</i> 4 (2001): 182–96.
    <a href="https://doi.org/10.1112/s1461157000000851">https://doi.org/10.1112/s1461157000000851</a>.'
  ieee: 'J. Klüners and G. Malle, “A Database for Field Extensions of the Rationals,”
    <i>LMS Journal of Computation and Mathematics</i>, vol. 4, pp. 182–196, 2001,
    doi: <a href="https://doi.org/10.1112/s1461157000000851">10.1112/s1461157000000851</a>.'
  mla: Klüners, Jürgen, and Gunter Malle. “A Database for Field Extensions of the
    Rationals.” <i>LMS Journal of Computation and Mathematics</i>, vol. 4, Wiley,
    2001, pp. 182–96, doi:<a href="https://doi.org/10.1112/s1461157000000851">10.1112/s1461157000000851</a>.
  short: J. Klüners, G. Malle, LMS Journal of Computation and Mathematics 4 (2001)
    182–196.
date_created: 2022-12-23T09:56:22Z
date_updated: 2023-03-02T09:53:08Z
department:
- _id: '102'
doi: 10.1112/s1461157000000851
external_id:
  arxiv:
  - math/0102232
intvolume: '         4'
keyword:
- Computational Theory and Mathematics
- General Mathematics
language:
- iso: eng
page: 182-196
publication: LMS Journal of Computation and Mathematics
publication_identifier:
  issn:
  - 1461-1570
publication_status: published
publisher: Wiley
status: public
title: A Database for Field Extensions of the Rationals
type: journal_article
user_id: '93826'
volume: 4
year: '2001'
...
---
_id: '16513'
author:
- first_name: P. J.
  full_name: Aston, P. J.
  last_name: Aston
- first_name: M.
  full_name: Dellnitz, M.
  last_name: Dellnitz
citation:
  ama: 'Aston PJ, Dellnitz M. The Computation of Lyapunov Exponents via Spatial Integration
    Using Vector Norms. In: <i>Equadiff 99</i>. ; 2000. doi:<a href="https://doi.org/10.1142/9789812792617_0196">10.1142/9789812792617_0196</a>'
  apa: Aston, P. J., &#38; Dellnitz, M. (2000). The Computation of Lyapunov Exponents
    via Spatial Integration Using Vector Norms. In <i>Equadiff 99</i>. <a href="https://doi.org/10.1142/9789812792617_0196">https://doi.org/10.1142/9789812792617_0196</a>
  bibtex: '@inbook{Aston_Dellnitz_2000, title={The Computation of Lyapunov Exponents
    via Spatial Integration Using Vector Norms}, DOI={<a href="https://doi.org/10.1142/9789812792617_0196">10.1142/9789812792617_0196</a>},
    booktitle={Equadiff 99}, author={Aston, P. J. and Dellnitz, M.}, year={2000} }'
  chicago: Aston, P. J., and M. Dellnitz. “The Computation of Lyapunov Exponents via
    Spatial Integration Using Vector Norms.” In <i>Equadiff 99</i>, 2000. <a href="https://doi.org/10.1142/9789812792617_0196">https://doi.org/10.1142/9789812792617_0196</a>.
  ieee: P. J. Aston and M. Dellnitz, “The Computation of Lyapunov Exponents via Spatial
    Integration Using Vector Norms,” in <i>Equadiff 99</i>, 2000.
  mla: Aston, P. J., and M. Dellnitz. “The Computation of Lyapunov Exponents via Spatial
    Integration Using Vector Norms.” <i>Equadiff 99</i>, 2000, doi:<a href="https://doi.org/10.1142/9789812792617_0196">10.1142/9789812792617_0196</a>.
  short: 'P.J. Aston, M. Dellnitz, in: Equadiff 99, 2000.'
date_created: 2020-04-15T07:53:09Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1142/9789812792617_0196
language:
- iso: eng
publication: Equadiff 99
publication_identifier:
  isbn:
  - '9789810243593'
  - '9789812792617'
publication_status: published
status: public
title: The Computation of Lyapunov Exponents via Spatial Integration Using Vector
  Norms
type: book_chapter
user_id: '15701'
year: '2000'
...