

Preprint 26/2011
Topological bifurcations of minimal invariant sets for set-valued dynamical systems
Jeroen S. W. Lamb, Martin Rasmussen, and Christian S. Rodrigues
Contact the author: Please use for correspondence this email.
Submission date: 25. May. 2011
Pages: 17
published in: Proceedings of the American Mathematical Society, 143 (2015) 9, p. 3927-3937
DOI number (of the published article): 10.1090/S0002-9939-2015-12544-0
Bibtex
MSC-Numbers: 37G35, 37H20, 37C70, 49K21, 37B25, 34A60
Keywords and phrases: Set-valued dynamical systems, random dynamical systems, Control
Download full preprint: PDF (461 kB)
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.