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2011.1: Invariant measures of the border collision normal form

2011.1: Paul Glendinning (2011) Invariant measures of the border collision normal form.

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Abstract

The border collision normal form is a two dimensional continuous, piecewise affine map which arises naturally in models where the dynamics is defined by different systems of equations in different regions of phase space, but which are continuous across the boundaries between regions. There are theorems which establish the existence of invariant measures for chaotic attractors of these systems, but the conditions are hard to establish analytically. By verifying these conditions numerically it is possible to describe regions of parameter space for which invariant measures do exist (up to numerical confidence) and compare this with what is known about the dynamics in these regions.

Item Type:MIMS Preprint
Uncontrolled Keywords:border collision bifurcation, chaotic attractor, invariant measure, hybrid system, CICADA
Subjects:MSC 2000 > 37 Dynamical systems and ergodic theory
MIMS number:2011.1
Deposited By:Professor Paul Glendinning
Deposited On:04 January 2011

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