Dynamics of a Continuous Piecewise Affine Map of the Square
Dynamical Systems
2013-12-31 v1
Abstract
We present a one-parameter family of continuous, piecewise affine, area preserving maps of the square, which are inspired by a dynamical system in game theory. Interested in the coexistence of stochastic and (quasi-)periodic behaviour, we investigate invariant annuli separated by invariant circles. For certain parameter values, we explicitly construct invariant circles both of rational and irrational rotation numbers, and present numerical experiments of the dynamics on the annuli bounded by these circles.
Keywords
Cite
@article{arxiv.1305.4282,
title = {Dynamics of a Continuous Piecewise Affine Map of the Square},
author = {Georg Ostrovski},
journal= {arXiv preprint arXiv:1305.4282},
year = {2013}
}
Comments
15 pages, 9 figures