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Hyperbolicity of renormalization for maps with multiple breaks
Abstract
We construct hyperbolic horseshoes for piecewise-analytic homeomorphisms of the circle with {\it multiple} break-type singularities, under the assumptions of bounded type rotation numbers and bounded geometry -- provided the sizes of the breaks are uniformly small. As a consequence, we obtain a C1+α-rigidity result for such maps and prove that rigidity classes are analytic submanifolds.
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BibTeX
@misc{goncharuk2026hyperbolicity,
title = {{Hyperbolicity of renormalization for maps with multiple breaks}},
author = {Nataliya Goncharuk and Igors Gorbovickis and Michael Yampolsky},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.14848},
eprint = {2609.14848},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.14848},
}
RIS
TY - UNPB
TI - Hyperbolicity of renormalization for maps with multiple breaks
AU - Nataliya Goncharuk
AU - Igors Gorbovickis
AU - Michael Yampolsky
PY - 2026
DA - 2026/09/13
PB - arXiv
DO - 10.48550/arxiv.2609.14848
UR - https://arxiv.org/abs/2609.14848
AB - We construct hyperbolic horseshoes for piecewise-analytic homeomorphisms of the circle with {\it multiple} break-type singularities, under the assumptions of bounded type rotation numbers and bounded geometry -- provided the sizes of the breaks are uniformly small. As a consequence, we obtain a C^1+α-rigidity result for such maps and prove that rigidity classes are analytic submanifolds.
ER -