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2010.100: Two dimensional attractors in the border collision normal form

2010.100: Paul Glendinning and Chi Hong Wong (2010) Two dimensional attractors in the border collision normal form.

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Abstract

New techniques are developed to show that the two-dimensional normal form for codimension one border collision bifurcations of fixed points of discrete time piecewise smooth dynamical systems has attractors which are themselves two dimensional. This makes it possible to prove the existence of these attractors for a countable set of parameter values which cannot be treated using the essentially one-dimensional methods in the literature.

Item Type:MIMS Preprint
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CICADA

Uncontrolled Keywords:border collision bifurcation, attractor, piecewise smooth systems, piecewise affine systems
Subjects:MSC 2000 > 37 Dynamical systems and ergodic theory
PACS 2003 > 05 Statistical physics, thermodynamics, and nonlinear dynamical systems
MIMS number:2010.100
Deposited By:Professor Paul Glendinning
Deposited On:17 November 2010

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