Corpus ID: 237571414

# Renormalisation of the two-dimensional border-collision normal form

@inproceedings{Ghosh2021RenormalisationOT,
title={Renormalisation of the two-dimensional border-collision normal form},
author={Indrani Ghosh and David J. W. Simpson},
year={2021}
}
• Published 19 September 2021
• Physics, Mathematics
We study the two-dimensional border-collision normal form (a four-parameter family of continuous, piecewise-linear maps on R2) 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.

#### Figures and Tables from this paper

Robust Devaney chaos in the two-dimensional border-collision normal form
The collection of all non-degenerate, continuous, two-piece, piecewise-linear maps on R2 can be reduced to a four-parameter family known as the two-dimensional bordercollision normal form. We proveExpand

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