@article{16684,
author = {Dellnitz, M. and Sch�tze, O. and Hestermeyer, T.},
issn = {0022-3239},
journal = {Journal of Optimization Theory and Applications},
pages = {113--136},
title = {{Covering Pareto Sets by Multilevel Subdivision Techniques}},
doi = {10.1007/s10957-004-6468-7},
year = {2005},
}
@article{16557,
abstract = { We combine the techniques of almost invariant sets (using tree structured box elimination and graph partitioning algorithms) with invariant manifold and lobe dynamics techniques. The result is a new computational technique for computing key dynamical features, including almost invariant sets, resonance regions as well as transport rates and bottlenecks between regions in dynamical systems. This methodology can be applied to a variety of multibody problems, including those in molecular modeling, chemical reaction rates and dynamical astronomy. In this paper we focus on problems in dynamical astronomy to illustrate the power of the combination of these different numerical tools and their applicability. In particular, we compute transport rates between two resonance regions for the three-body system consisting of the Sun, Jupiter and a third body (such as an asteroid). These resonance regions are appropriate for certain comets and asteroids. },
author = {Dellnitz, Michael and Junge, Oliver and Koon, Wang Sang and Lekien, Francois and Lo, Martin W. and Marsden, Jerrold E. and Padberg, Kathrin and Preis, Robert and Ross, Shane D. and Thiere, Bianca},
issn = {0218-1274},
journal = {International Journal of Bifurcation and Chaos},
pages = {699--727},
title = {{Transport in Dynamical Astronomy and Multibody Problems}},
doi = {10.1142/s0218127405012545},
year = {2005},
}
@article{16627,
abstract = { The computation of global invariant manifolds has seen renewed interest in recent years. We survey different approaches for computing a global stable or unstable manifold of a vector field, where we concentrate on the case of a two-dimensional manifold. All methods are illustrated with the same example — the two-dimensional stable manifold of the origin in the Lorenz system. },
author = {Krauskopf, B. and Osinga, H. M. and Doedel, E. J. and Henderson, M. E. and Guckenheimer, J. and Vladimirsky, A. and Dellnitz, M. and Junge, O.},
issn = {0218-1274},
journal = {International Journal of Bifurcation and Chaos},
pages = {763--791},
title = {{A Survey of Methods for Computing (un)stable Manifolds of Vector Fields}},
doi = {10.1142/s0218127405012533},
year = {2005},
}
@article{16558,
author = {Dellnitz, Michael and Junge, Oliver and Lo, Martin W. and Marsden, Jerrold E. and Padberg, Kathrin and Preis, Robert and Ross, Shane D. and Thiere, Bianca},
issn = {0031-9007},
journal = {Physical Review Letters},
title = {{Transport of Mars-Crossing Asteroids from the Quasi-Hilda Region}},
doi = {10.1103/physrevlett.94.231102},
year = {2005},
}
@inproceedings{16628,
author = {Krishnamurthy, A. and Preis, R.},
booktitle = {19th IEEE International Parallel and Distributed Processing Symposium},
isbn = {0769523129},
title = {{Satellite Formation, a Mobile Sensor Network in Space}},
doi = {10.1109/ipdps.2005.387},
year = {2005},
}
@inproceedings{16631,
author = {Li, R. and Pottharst, A. and Frohieke, N. and Becker, J. and Witting, K. and Dellnitz, M. and Znamenshchykov, O. and Feldmann, R.},
booktitle = {Twentieth Annual IEEE Applied Power Electronics Conference and Exposition, 2005. APEC 2005.},
isbn = {0780389751},
title = {{Design and implementation of a hybrid energy supply system for railway vehicles}},
doi = {10.1109/apec.2005.1452979},
year = {2005},
}
@article{16500,
author = {Chaudhuri, I. and Sertl, S. and Hajnal, Z. and Dellnitz, M. and Frauenheim, Th.},
issn = {0169-4332},
journal = {Applied Surface Science},
pages = {108--113},
title = {{Global optimization of silicon nanoclusters}},
doi = {10.1016/j.apsusc.2003.11.007},
year = {2004},
}
@inproceedings{16620,
author = {Junge, O. and Marsden, J.E. and Mezic, I.},
booktitle = {2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)},
isbn = {0780386825},
title = {{Uncertainty in the dynamics of conservative maps}},
doi = {10.1109/cdc.2004.1430379},
year = {2004},
}
@article{16587,
abstract = { 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 l2 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. },
author = {Elsässer, Robert and Monien, Burkhard and Preis, Robert and Frommer, Andreas},
issn = {0129-6264},
journal = {Parallel Processing Letters},
pages = {61--73},
title = {{Optimal Diffusion Schemes and Load Balancing on Product Graphs}},
doi = {10.1142/s0129626404001714},
year = {2004},
}
@article{16619,
author = {Junge, Oliver and Osinga, Hinke M.},
issn = {1292-8119},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {259--270},
title = {{A set oriented approach to global optimal control}},
doi = {10.1051/cocv:2004006},
year = {2004},
}
@article{16521,
author = {Bezrukov, S. and Elsässer, R. and Monien, B. and Preis, R. and Tillich, J.-P.},
issn = {0304-3975},
journal = {Theoretical Computer Science},
pages = {155--174},
title = {{New spectral lower bounds on the bisection width of graphs}},
doi = {10.1016/j.tcs.2004.03.059},
year = {2004},
}
@article{16527,
author = {Day, S. and Junge, O. and Mischaikow, K.},
issn = {1536-0040},
journal = {SIAM Journal on Applied Dynamical Systems},
pages = {117--160},
title = {{A Rigorous Numerical Method for the Global Analysis of Infinite-Dimensional Discrete Dynamical Systems}},
doi = {10.1137/030600210},
year = {2004},
}
@inbook{16543,
author = {Dellnitz, Michael and Preis, Robert},
booktitle = {Lecture Notes in Computer Science},
isbn = {9783540405542},
issn = {0302-9743},
title = {{Congestion and Almost Invariant Sets in Dynamical Systems}},
doi = {10.1007/3-540-45084-x_8},
year = {2003},
}
@article{16498,
author = {Aston, P. J. and Dellnitz, M.},
issn = {1364-5021},
journal = {Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences},
pages = {2933--2955},
title = {{Computation of the dominant Lyapunov exponent via spatial integration using matrix norms}},
doi = {10.1098/rspa.2003.1143},
year = {2003},
}
@inbook{16664,
author = {Schütze, Oliver},
booktitle = {Lecture Notes in Computer Science},
isbn = {9783540018698},
issn = {0302-9743},
title = {{A New Data Structure for the Nondominance Problem in Multi-objective Optimization}},
doi = {10.1007/3-540-36970-8_36},
year = {2003},
}
@inbook{16665,
author = {Schütze, Oliver and Mostaghim, Sanaz and Dellnitz, Michael and Teich, Jürgen},
booktitle = {Lecture Notes in Computer Science},
isbn = {9783540018698},
issn = {0302-9743},
title = {{Covering Pareto Sets by Multilevel Evolutionary Subdivision Techniques}},
doi = {10.1007/3-540-36970-8_9},
year = {2003},
}
@article{16600,
author = {Froyland, Gary and Dellnitz, Michael},
issn = {1064-8275},
journal = {SIAM Journal on Scientific Computing},
pages = {1839--1863},
title = {{Detecting and Locating Near-Optimal Almost-Invariant Sets and Cycles}},
doi = {10.1137/s106482750238911x},
year = {2003},
}
@article{16586,
author = {Elsässer, Robert and Monien, Burkhard and Preis, Robert},
issn = {1432-4350},
journal = {Theory of Computing Systems},
pages = {305--320},
title = {{Diffusion Schemes for Load Balancing on Heterogeneous Networks}},
doi = {10.1007/s00224-002-1056-4},
year = {2002},
}
@article{16556,
author = {Dellnitz, M.},
issn = {0272-4979},
journal = {IMA Journal of Numerical Analysis},
pages = {167--185},
title = {{Finding zeros by multilevel subdivision techniques}},
doi = {10.1093/imanum/22.2.167},
year = {2002},
}
@inbook{16538,
author = {Dellnitz, Michael and Junge, Oliver},
booktitle = {Handbook of Dynamical Systems},
isbn = {9780444501684},
issn = {1874-575X},
title = {{Set Oriented Numerical Methods for Dynamical Systems}},
doi = {10.1016/s1874-575x(02)80026-1},
year = {2002},
}
@inbook{16598,
author = {Froyland, Gary},
booktitle = {Nonlinear Dynamics and Statistics},
isbn = {9781461266488},
title = {{Extracting Dynamical Behavior via Markov Models}},
doi = {10.1007/978-1-4612-0177-9_12},
year = {2001},
}
@article{16601,
author = {Froyland, Gary and Junge, Oliver and Ochs, Gunter},
issn = {0167-2789},
journal = {Physica D: Nonlinear Phenomena},
pages = {68--84},
title = {{Rigorous computation of topological entropy with respect to a finite partition}},
doi = {10.1016/s0167-2789(01)00216-0},
year = {2001},
}
@inbook{16555,
author = {Dellnitz, Michael and Froyland, Gary and Junge, Oliver},
booktitle = {Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems},
isbn = {9783642625244},
title = {{The Algorithms Behind GAIO — Set Oriented Numerical Methods for Dynamical Systems}},
doi = {10.1007/978-3-642-56589-2_7},
year = {2001},
}
@article{16617,
author = {Junge, Oliver},
issn = {1468-9367},
journal = {Dynamical Systems},
pages = {213--222},
title = {{An adaptive subdivision technique for the approximation of attractors and invariant measures: proof of convergence}},
doi = {10.1080/14689360109696233},
year = {2001},
}
@inbook{16513,
author = {Aston, P. J. and Dellnitz, M.},
booktitle = {Equadiff 99},
isbn = {9789810243593},
title = {{The Computation of Lyapunov Exponents via Spatial Integration Using Vector Norms}},
doi = {10.1142/9789812792617_0196},
year = {2000},
}
@inbook{16553,
author = {Dellnitz, Michael and Froyland, Gary and Sertl, Stefan},
booktitle = {Equadiff 99},
isbn = {9789810243593},
title = {{A Conjecture on the Existence of Isolated Eigenvalues of the Perron-Frobenius Operator}},
doi = {10.1142/9789812792617_0199},
year = {2000},
}
@inbook{16616,
author = {Junge, Oliver},
booktitle = {Equadiff 99},
isbn = {9789810243593},
title = {{Rigorous discretization of subdivision techniques}},
doi = {10.1142/9789812792617_0178},
year = {2000},
}
@inbook{17018,
author = {Dellnitz, Michael and Junge, Oliver and Rumpf, Martin and Strzodka, Robert},
booktitle = {Equadiff 99},
isbn = {9789810243593},
pages = {1053----1059},
title = {{The computation of an unstable invariant set inside a cylinder containing a knotted flow}},
doi = {10.1142/9789812792617_0204},
year = {2000},
}
@article{16554,
author = {Dellnitz, Michael and Froyland, Gary and Sertl, Stefan},
issn = {0951-7715},
journal = {Nonlinearity},
pages = {1171--1188},
title = {{On the isolated spectrum of the Perron-Frobenius operator}},
doi = {10.1088/0951-7715/13/4/310},
year = {2000},
}
@article{16537,
author = {Dellnitz, Michael and Junge, Oliver},
issn = {0036-1429},
journal = {SIAM Journal on Numerical Analysis},
pages = {491--515},
title = {{On the Approximation of Complicated Dynamical Behavior}},
doi = {10.1137/s0036142996313002},
year = {1999},
}
@article{17017,
author = {Bürkle, David and Dellnitz, Michael and Junge, Oliver and Rumpf, Martin and Spielberg, Michael},
journal = {Proceedings of Visualization 99},
title = {{Visualizing Complicated Dynamics}},
year = {1999},
}
@inbook{16584,
author = {Deuflhard, Peter and Dellnitz, Michael and Junge, Oliver and Schütte, Christof},
booktitle = {Computational Molecular Dynamics: Challenges, Methods, Ideas},
isbn = {9783540632429},
issn = {1439-7358},
title = {{Computation of Essential Molecular Dynamics by Subdivision Techniques}},
doi = {10.1007/978-3-642-58360-5_5},
year = {1999},
}
@article{16511,
author = {Aston, Philip J. and Dellnitz, Michael},
issn = {0045-7825},
journal = {Computer Methods in Applied Mechanics and Engineering},
pages = {223--237},
title = {{The computation of lyapunov exponents via spatial integration with application to blowout bifurcations}},
doi = {10.1016/s0045-7825(98)00196-0},
year = {1999},
}
@article{16536,
author = {Dellnitz, Michael and Junge, Oliver},
issn = {1432-9360},
journal = {Computing and Visualization in Science},
pages = {63--68},
title = {{An adaptive subdivision technique for the approximation of attractors and invariant measures}},
doi = {10.1007/s007910050006},
year = {1998},
}
@article{17015,
author = {Dellnitz, Michael and Hohmann, Andreas},
issn = {0029-599X},
journal = {Numerische Mathematik},
pages = {293--317},
title = {{A subdivision algorithm for the computation of unstable manifolds and global attractors}},
doi = {10.1007/s002110050240},
volume = {75},
year = {1997},
}
@article{16614,
author = {Guder, Rabbijah and Dellnitz, Michael and Kreuzer, Edwin},
issn = {0960-0779},
journal = {Chaos, Solitons & Fractals},
pages = {525--534},
title = {{An adaptive method for the approximation of the generalized cell mapping}},
doi = {10.1016/s0960-0779(96)00118-x},
year = {1997},
}
@article{16552,
author = {Dellnitz, Michael and Hohmann, Andreas and Junge, Oliver and Rumpf, Martin},
issn = {1054-1500},
journal = {Chaos: An Interdisciplinary Journal of Nonlinear Science},
pages = {221--228},
title = {{Exploring invariant sets and invariant measures}},
doi = {10.1063/1.166223},
year = {1997},
}
@article{16535,
abstract = { Recently multilevel subdivision techniques have been introduced in the numerical investigation of complicated dynamical behavior. We illustrate the applicability and efficiency of these methods by a detailed numerical study of Chua's circuit. In particular we will show that there exist two regions in phase space which are almost invariant in the sense that typical trajectories stay inside each of these sets on average for quite a long time. },
author = {Dellnitz, Michael and Junge, Oliver},
issn = {0218-1274},
journal = {International Journal of Bifurcation and Chaos},
pages = {2475--2485},
title = {{Almost Invariant Sets in Chua's Circuit}},
doi = {10.1142/s0218127497001655},
year = {1997},
}
@inbook{16533,
author = {Dellnitz, Michael and Hohmann, Andreas},
booktitle = {Nonlinear Dynamical Systems and Chaos},
isbn = {9783034875202},
title = {{The Computation of Unstable Manifolds Using Subdivision and Continuation}},
doi = {10.1007/978-3-0348-7518-9_21},
year = {1996},
}
@article{16550,
author = {Dellnitz, Michael and Field, Michael and Golubitsky, Martin and Ma, Jun and Hohmann, Andreas},
issn = {0218-1274},
journal = {International Journal of Bifurcation and Chaos},
pages = {1243--1247},
title = {{Cycling Chaos}},
doi = {10.1142/s0218127495000909},
year = {1995},
}
@article{16532,
author = {Dellnitz, M and Heinrich, C},
issn = {0951-7715},
journal = {Nonlinearity},
pages = {1039--1066},
title = {{Admissible symmetry increasing bifurcations}},
doi = {10.1088/0951-7715/8/6/009},
year = {1995},
}
@article{16551,
abstract = { Spiral patterns have been observed experimentally, numerically, and theoretically in a variety of systems. It is often believed that these spiral wave patterns can occur only in systems of reaction–diffusion equations. We show, both theoretically (using Hopf bifurcation techniques) and numerically (using both direct simulation and continuation of rotating waves) that spiral wave patterns can appear in a single reaction–diffusion equation [ in u(x, t)] on a disk, if one assumes "spiral" boundary conditions (ur = muθ). Spiral boundary conditions are motivated by assuming that a solution is infinitesimally an Archimedian spiral near the boundary. It follows from a bifurcation analysis that for this form of spirals there are no singularities in the spiral pattern (technically there is no spiral tip) and that at bifurcation there is a steep gradient between the "red" and "blue" arms of the spiral. },
author = {Dellnitz, Michael and Golubitsky, Martin and Hohmann, Andreas and Stewart, Ian},
issn = {0218-1274},
journal = {International Journal of Bifurcation and Chaos},
pages = {1487--1501},
title = {{Spirals in Scalar Reaction–Diffusion Equations}},
doi = {10.1142/s0218127495001149},
year = {1995},
}
@inbook{16611,
author = {Golubitsky, Martin and Marsden, Jerrold and Stewart, Ian and Dellnitz, Michael},
booktitle = {Normal Forms and Homoclinic Chaos},
isbn = {9780821803264},
title = {{The constrained Liapunov-Schmidt procedure and periodic orbits}},
doi = {10.1090/fic/004/05},
year = {1995},
}
@article{16510,
abstract = { In an array of coupled oscillators, synchronous chaos may occur in the sense that all the oscillators behave identically although the corresponding motion is chaotic. When a parameter is varied this fully symmetric dynamical state can lose its stability, and the main purpose of this paper is to investigate which type of dynamical behavior is expected to be observed once the loss of stability has occurred. The essential tool is a classification of Lyapunov exponents based on the symmetry of the underlying problem. This classification is crucial in the derivation of the analytical results but it also allows an efficient computation of the dominant Lyapunov exponent associated with each symmetry type. We show how these dominant exponents determine the stability of invariant sets possessing various instantaneous symmetries, and this leads to the idea of symmetry breaking bifurcations of chaotic attractors. Finally, the results and ideas are illustrated for several systems of coupled oscillators. },
author = {Aston, Philip J. and Dellnitz, Michael},
issn = {0218-1274},
journal = {International Journal of Bifurcation and Chaos},
pages = {1643--1676},
title = {{Symmetry Breaking Bifurcations of Chaotic Attractors}},
doi = {10.1142/s021812749500123x},
year = {1995},
}
@article{16542,
author = {Dellnitz, M and Melbourne, I},
issn = {0951-7715},
journal = {Nonlinearity},
pages = {1067--1075},
title = {{A note on the shadowing lemma and symmetric periodic points}},
doi = {10.1088/0951-7715/8/6/010},
year = {1995},
}
@inbook{16549,
author = {Dellnitz, Michael and Golubitsky, Martin and Nicol, Matthew},
booktitle = {Trends and Perspectives in Applied Mathematics},
isbn = {9781461269243},
issn = {0066-5452},
title = {{Symmetry of Attractors and the Karhunen-Loève Decomposition}},
doi = {10.1007/978-1-4612-0859-4_4},
year = {1994},
}
@inbook{16544,
author = {Dellnitz, Michael and Scheurle, Jürgen},
booktitle = {Dynamics, Bifurcation and Symmetry},
isbn = {9789401044134},
title = {{Eigenvalue Movement for a Class of Reversible Hamiltonian Systems with Three Degrees of Freedom}},
doi = {10.1007/978-94-011-0956-7_9},
year = {1994},
}
@article{16541,
author = {Dellnitz, Michael and Melbourne, Ian},
issn = {0377-0427},
journal = {Journal of Computational and Applied Mathematics},
pages = {249--259},
title = {{Generic movement of eigenvalues for equivariant self-adjoint matrices}},
doi = {10.1016/0377-0427(94)90032-9},
year = {1994},
}
@article{17014,
author = {Dellnitz, Michael},
journal = {Schlaglichter der Forschung: Zum 75. Jahrestag der Universität Hamburg},
pages = {411--428},
title = {{Collisions of chaotic attractors}},
year = {1994},
}
@article{16633,
abstract = {AbstractWe obtain normal forms for infinitesimally symplectic matrices (or linear Hamiltonian vector fields) that commute with the symplectic action of a compact Lie group of symmetries. In doing so we extend Williamson's theorem on normal forms when there is no symmetry present.Using standard representation-theoretic results the symmetry can be factored out and we reduce to finding normal forms over a real division ring. There are three real division rings consisting of the real, complex and quaternionic numbers. Of these, only the real case is covered in Williamson's original work.},
author = {Melbourne, Ian and Dellnitz, Michael},
issn = {0305-0041},
journal = {Mathematical Proceedings of the Cambridge Philosophical Society},
pages = {235--268},
title = {{Normal forms for linear Hamiltonian vector fields commuting with the action of a compact Lie group}},
doi = {10.1017/s0305004100071577},
year = {1993},
}
@article{16518,
author = {Barany, Ernest and Dellnitz, Michael and Golubitsky, Martin},
issn = {0167-2789},
journal = {Physica D: Nonlinear Phenomena},
pages = {66--87},
title = {{Detecting the symmetry of attractors}},
doi = {10.1016/0167-2789(93)90198-a},
year = {1993},
}
@article{16634,
author = {Melbourne, Ian and Dellnitz, Michael and Golubitsky, Martin},
issn = {0003-9527},
journal = {Archive for Rational Mechanics and Analysis},
pages = {75--98},
title = {{The structure of symmetric attractors}},
doi = {10.1007/bf00386369},
year = {1993},
}
@article{17013,
author = {Dellnitz, Michael},
journal = {Lectures in Applied Mathematics},
pages = {163--169},
title = {{The equivariant Darboux theorem}},
volume = {29},
year = {1993},
}
@article{16548,
author = {Dellnitz, M and Melbourne, I and Marsden, J E},
issn = {0951-7715},
journal = {Nonlinearity},
pages = {979--996},
title = {{Generic bifurcation of Hamiltonian vector fields with symmetry}},
doi = {10.1088/0951-7715/5/4/008},
year = {1992},
}
@article{17012,
author = {Dellnitz, Michael},
journal = {IMA Journal of Numerical Analysis},
number = {3},
pages = {429--455},
title = {{Computational bifurcation of periodic solutions in systems with symmetry}},
doi = {10.1093/imanum/12.3.429},
volume = {12},
year = {1992},
}
@inbook{16546,
author = {Dellnitz, Michael and Golubitsky, Martin and Melbourne, Ian},
booktitle = {Bifurcation and Symmetry},
isbn = {9783034875387},
title = {{Mechanisms of Symmetry Creation}},
doi = {10.1007/978-3-0348-7536-3_9},
year = {1992},
}
@inbook{16547,
author = {Dellnitz, Michael and Marsden, Jerrold E. and Melbourne, Ian and Scheurle, Jürgen},
booktitle = {Bifurcation and Symmetry},
isbn = {9783034875387},
title = {{Generic Bifurcations of Pendula}},
doi = {10.1007/978-3-0348-7536-3_10},
year = {1992},
}
@article{16682,
author = {Dellnitz, Michael and Werner, Bodo},
issn = {0377-0427},
journal = {Journal of Computational and Applied Mathematics},
pages = {97--123},
title = {{Computational methods for bifurcation problems with symmetries—with special attention to steady state and Hopf bifurcation points}},
doi = {10.1016/0377-0427(89)90150-7},
year = {1989},
}