Construction of Invariant Curves for Some Piecewise Isometries

Fuente: arXiv
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Main Authors: Cockram, Noah, Ashwin, Peter, Rodrigues, Ana
Format: Preprint
Published: 2023
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author Cockram, Noah
Ashwin, Peter
Rodrigues, Ana
author_facet Cockram, Noah
Ashwin, Peter
Rodrigues, Ana
contents We establish conditions for the existence of a family of piecewise linear invariant curves in a two-parameter family of piecewise isometries on the upper half-plane known as Translated Cone Exchange Transformations. We show that these curves are embeddings of interval exchange transformations and give rise to layers of invariant regions. We also show the existence of a trapezoidal piecewise isometry for which the dynamics on the top and bottom edges are distinct 2-interval exchange transformations.
format Preprint
id arxiv_https___arxiv_org_abs_2312_17412
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Construction of Invariant Curves for Some Piecewise Isometries
Cockram, Noah
Ashwin, Peter
Rodrigues, Ana
Dynamical Systems
37E05
We establish conditions for the existence of a family of piecewise linear invariant curves in a two-parameter family of piecewise isometries on the upper half-plane known as Translated Cone Exchange Transformations. We show that these curves are embeddings of interval exchange transformations and give rise to layers of invariant regions. We also show the existence of a trapezoidal piecewise isometry for which the dynamics on the top and bottom edges are distinct 2-interval exchange transformations.
title Construction of Invariant Curves for Some Piecewise Isometries
topic Dynamical Systems
37E05
url https://arxiv.org/abs/2312.17412