Invariant measures for the n-dimensional border collision normal form

Glendinning, Paul (2014) Invariant measures for the n-dimensional border collision normal form. International Journal of Bifurcations and Chaos.

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The border collision normal form is a continuous piecewise affine map of $\BR^n$ with applications in piecewise smooth bifurcation theory. We show that these maps have absolutely continuous invariant measures for an open set of parameter space and hence that the attractors have Hausdorff (fractal) dimension $n$. If $n = 2$ the attractors have topological dimension two, i.e. they contain open sets, and if $n>2$ then they have topological dimension $n$ generically.

Item Type: Article
Uncontrolled Keywords: border collision bifurcation, attractor, piecewise smooth systems, piecewise affine systems
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 37 Dynamical systems and ergodic theory
Depositing User: Professor Paul Glendinning
Date Deposited: 17 Feb 2015
Last Modified: 20 Oct 2017 14:13

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