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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
26/2011

Topological bifurcations of minimal invariant sets for set-valued dynamical systems

Jeroen S. W. Lamb, Martin Rasmussen and Christian S. Rodrigues

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.

Received:
May 25, 2011
Published:
May 25, 2011
MSC Codes:
37G35, 37H20, 37C70, 49K21, 37B25, 34A60
Keywords:
Set-valued dynamical systems, random dynamical systems, Control

Related publications

inJournal
2015 Repository Open Access
Jeroen S. W. Lamb, Martin Rasmussen and Christian S. Rodrigues

Topological bifurcations of minimal invariant sets for set-valued dynamical systems

In: Proceedings of the American Mathematical Society, 143 (2015) 9, pp. 3927-3937