Bifurcations of Snap-back Repellers with application to Border-Collision Bifurcations

Glendinning, Paul (2009) Bifurcations of Snap-back Repellers with application to Border-Collision Bifurcations. [MIMS Preprint]

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Abstract

The bifurcation theory of snap-back repellers in hybrid dynamical systems is developed. Infinite sequences of bifurcations are shown to arise due to the creation of snap-back repellers in non-invertible maps. These are analogous to the cascades of bifurcations known to occur close to homoclinic tangencies for diffeomorphisms. The theoretical results are illustrated with reference to bifurcations in the normal form for border-collision bifurcations.

Item Type: MIMS Preprint
Uncontrolled Keywords: CICADA
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 37 Dynamical systems and ergodic theory
MSC 2010, the AMS's Mathematics Subject Classification > 39 Difference and functional equations
Depositing User: Professor Paul Glendinning
Date Deposited: 11 May 2009
Last Modified: 08 Nov 2017 18:18
URI: http://eprints.maths.manchester.ac.uk/id/eprint/1264

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