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Title: Bifurcations of set-valued dynamical systems
Author: Athorne, Alexander
ISNI:       0000 0004 7427 7352
Awarding Body: Imperial College London
Current Institution: Imperial College London
Date of Award: 2018
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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.
Supervisor: Rasmussen, Martin ; Lamb, Jeroen Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral