Topological bifurcations of minimal invariant sets for set-valued dynamical systems
Dynamical Systems
2022-02-10 v2 Classical Analysis and ODEs
Abstract
We discuss the dependence of set-valued dynamical systems on parameters. Under mild assumptions which are often satisfied for random dynamical systems with bounded noise and control systems, we establish the fact that topological bifurcations of minimal invariant sets are discontinuous with respect to the Hausdorff metric, taking the form of lower semi-continuous explosions and instantaneous appearances. We also characterise these transitions by properties of Morse-like decompositions.
Keywords
Cite
@article{arxiv.1105.5018,
title = {Topological bifurcations of minimal invariant sets for set-valued dynamical systems},
author = {Jeroen S. W. Lamb and Martin Rasmussen and Christian S. Rodrigues},
journal= {arXiv preprint arXiv:1105.5018},
year = {2022}
}
Comments
10 pages