• 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}
}
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. 
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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 border-collision normal form. We prove…

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