Bifurcation from stable fixed point to $N$-dimensional attractor in the border collision normal form

Glendinning, Paul (2015) Bifurcation from stable fixed point to $N$-dimensional attractor in the border collision normal form. [MIMS Preprint]

PDF bifntondim.pdf Download (82kB)

Abstract

The $N$-dimensional border collision normal form describes bifurcations of piecewise smooth systems. It is shown that there is an open set of parameters such that on one side of the bifurcation the map has a stable fixed point and on the other an attractor with Hausdorff dimension $N$. For generic parameters this attractor contains open sets and hence has topological dimension equal to $N$.

Item Type:	MIMS Preprint
Uncontrolled Keywords:	border collision bifurcation, attractor, piecewise smooth systems, piecewise affine systems, high dimensional attractors
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 37 Dynamical systems and ergodic theory PACS 2010, the AIP's Physics and Astronomy Classification Scheme > 00 GENERAL PHYSICS > 05 Statistical physics, thermodynamics, and nonlinear dynamical systems
Depositing User:	Professor Paul Glendinning
Date Deposited:	24 Feb 2015
Last Modified:	08 Nov 2017 18:18
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/2250

Actions (login required)

View Item