---
_id: '16708'
abstract:
- lang: eng
text: " In this work we extend the novel framework developed by Dellnitz, Hessel-von
Molo, and Ziessler to\r\nthe computation of finite dimensional unstable manifolds
of infinite dimensional dynamical systems.\r\nTo this end, we adapt a set-oriented
continuation technique developed by Dellnitz and Hohmann for\r\nthe computation
of such objects of finite dimensional systems with the results obtained in the
work\r\nof Dellnitz, Hessel-von Molo, and Ziessler. We show how to implement this
approach for the analysis\r\nof partial differential equations and illustrate
its feasibility by computing unstable manifolds of the\r\none-dimensional Kuramoto--Sivashinsky
equation as well as for the Mackey--Glass delay differential\r\nequation.\r\n"
author:
- first_name: Adrian
full_name: Ziessler, Adrian
last_name: Ziessler
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Raphael
full_name: Gerlach, Raphael
id: '32655'
last_name: Gerlach
citation:
ama: Ziessler A, Dellnitz M, Gerlach R. The Numerical Computation of Unstable Manifolds
for Infinite Dimensional Dynamical Systems by Embedding Techniques. SIAM Journal
on Applied Dynamical Systems. 2019;18(3):1265-1292. doi:10.1137/18m1204395
apa: Ziessler, A., Dellnitz, M., & Gerlach, R. (2019). The Numerical Computation
of Unstable Manifolds for Infinite Dimensional Dynamical Systems by Embedding
Techniques. SIAM Journal on Applied Dynamical Systems, 18(3), 1265–1292.
https://doi.org/10.1137/18m1204395
bibtex: '@article{Ziessler_Dellnitz_Gerlach_2019, title={The Numerical Computation
of Unstable Manifolds for Infinite Dimensional Dynamical Systems by Embedding
Techniques}, volume={18}, DOI={10.1137/18m1204395},
number={3}, journal={SIAM Journal on Applied Dynamical Systems}, author={Ziessler,
Adrian and Dellnitz, Michael and Gerlach, Raphael}, year={2019}, pages={1265–1292}
}'
chicago: 'Ziessler, Adrian, Michael Dellnitz, and Raphael Gerlach. “The Numerical
Computation of Unstable Manifolds for Infinite Dimensional Dynamical Systems by
Embedding Techniques.” SIAM Journal on Applied Dynamical Systems 18, no.
3 (2019): 1265–92. https://doi.org/10.1137/18m1204395.'
ieee: 'A. Ziessler, M. Dellnitz, and R. Gerlach, “The Numerical Computation of Unstable
Manifolds for Infinite Dimensional Dynamical Systems by Embedding Techniques,”
SIAM Journal on Applied Dynamical Systems, vol. 18, no. 3, pp. 1265–1292,
2019, doi: 10.1137/18m1204395.'
mla: Ziessler, Adrian, et al. “The Numerical Computation of Unstable Manifolds for
Infinite Dimensional Dynamical Systems by Embedding Techniques.” SIAM Journal
on Applied Dynamical Systems, vol. 18, no. 3, 2019, pp. 1265–92, doi:10.1137/18m1204395.
short: A. Ziessler, M. Dellnitz, R. Gerlach, SIAM Journal on Applied Dynamical Systems
18 (2019) 1265–1292.
date_created: 2020-04-16T14:04:20Z
date_updated: 2023-11-17T13:13:09Z
department:
- _id: '101'
doi: 10.1137/18m1204395
intvolume: ' 18'
issue: '3'
language:
- iso: eng
main_file_link:
- url: https://epubs.siam.org/doi/epdf/10.1137/18M1204395
page: 1265-1292
publication: SIAM Journal on Applied Dynamical Systems
publication_identifier:
issn:
- 1536-0040
publication_status: published
status: public
title: The Numerical Computation of Unstable Manifolds for Infinite Dimensional Dynamical
Systems by Embedding Techniques
type: journal_article
user_id: '32655'
volume: 18
year: '2019'
...