title: Border collision bifurcations, snap-back repellers, and chaos.
abstract: The normal form for codimension 1 border collision bifurcations of fixed points of discrete time piecewise smooth dynamical systems is considered in the unstable case. We show that in appropriate parameter regions there is a snap-back repeller immediately after the bifurcation, and hence that the bifurcation creates chaos. Although the chaotic solutions are repellers they may explain observations, and this is illustrated through an example.
authors.affiliation: School of Mathematics and Centre for Interdisciplinary Computational and Dynamical Analysis (CICADA), University of Manchester, Manchester M13 9PL, United Kingdom. p.a.glendinning@manchester.ac.uk
authors.forename: Paul
authors.initials: P
authors.lastname: Glendinning
authors.forename: Chi Hong
authors.initials: CH
authors.lastname: Wong