On the sighting of unicorns: A variational approach to computing invariant sets in dynamical systems
Publication Year
2017
Type
Journal Article
Abstract
We propose to compute approximations to invariant sets in dynamical systems by minimizing an appropriate distance between a suitably selected finite set of points and its image under the dynamics. We demonstrate, through computational experiments, that this approach can successfully converge to approximations of (maximal) invariant sets of arbitrary topol., dimension, and stability, such as, e.g., saddle type invariant sets with complicated dynamics. We further propose to extend this approach by adding a Lennard-Jones type potential term to the objective function, which yields more evenly distributed approximating finite point sets, and illustrate the procedure through corresponding numerical experiments (c) 2017 American Institute of Physics.
Journal
Chaos
Volume
27
Pages
063102/1
ISBN
1089-76821054-1500
CAplus AN 2017:1488682; MEDLINE PMID: 28679234 (Journal; Article)