Renormalisation of the two-dimensional border-collision normal form

Abstract

We study the two-dimensional border-collision normal form (a four-parameter family of continuous, piecewise-linear maps on ${\mathbb{R}}^2$) 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.

Cited by in corpus (1)

• Robust Devaney chaos in the two-dimensional border-collision normal form