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arXiv · 2109.09242

Renormalisation of the two-dimensional border-collision normal form

Indranil Ghosh·David J. W. Simpson
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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.

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Indranil Ghosh, David J. W. Simpson. 2021-09-19. Renormalisation of the two-dimensional border-collision normal form. https://doi.org/10.1142/s0218127422501814

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