Renormalisation of the two-dimensional border-collision normal form
Chaotic Dynamics
2022-10-26 v1 Dynamical Systems
Abstract
We study the two-dimensional border-collision normal form (a four-parameter family of continuous, piecewise-linear maps on ) in the robust chaos parameter region of [S. Banerjee, J.A. Yorke, C. Grebogi, Robust Chaos, Phys. Rev. Lett. 80(14):3049--3052, 1998]. We use renormalisation to partition this region by the number of connected components of a chaotic Milnor attractor. This reveals previously undescribed bifurcation structure in a succinct way.
Cite
@article{arxiv.2109.09242,
title = {Renormalisation of the two-dimensional border-collision normal form},
author = {Indranil Ghosh and David J. W. Simpson},
journal= {arXiv preprint arXiv:2109.09242},
year = {2022}
}