Bifurcations of Set-Valued Dynamical Systems

Abstract

We study families of set-valued dynamical systems and show how minimal invariant sets depend on parameters. We give a variant on the definition of attractor repeller pairs and obtain a different version of the Conley decomposition theorem. Under mild conditions on these systems we show that minimal invariant sets are related to a variation on the definition of chain components we call orbitally connected sets. We show for such systems that bifurcations can occur as a result of two orbitally connected sets colliding.