English

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 R2\mathbb{R}^2) 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.

Keywords

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}
}
R2 v1 2026-06-24T06:07:16.419Z