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

Lamb, Jeroen; Rasmussen, Martin; Rodrigues, Christian

doi:10.1090/S0002-9939-2015-12544-0

Topological bifurcations of minimal invariant sets for set-valued dynamical systems
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by Jeroen S. W. Lamb, Martin Rasmussen and Christian S. Rodrigues PDF

Proc. Amer. Math. Soc. 143 (2015), 3927-3937 Request permission

Abstract:

We discuss the dependence of set-valued dynamical systems on parameters. Under mild assumptions which are naturally 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.

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