Invariant measures for the n-dimensional border collision normal form

Glendinning, Paul (2014) Invariant measures for the n-dimensional border collision normal form. [MIMS Preprint]

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Abstract

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:	MIMS Preprint
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:	27 Jul 2015
Last Modified:	08 Nov 2017 18:18
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/2348

Available Versions of this Item

• Invariant measures for the n-dimensional border collision normal form. (deposited 17 Feb 2015)
  • Invariant measures for the n-dimensional border collision normal form. (deposited 27 Jul 2015) [Currently Displayed]

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