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

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

2011-05-25

arxiv.org/abs/1105.5018v1

Mathematics

Dynamical Systems

15 pages, 3 figures

Scientific paper

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.

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