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arXiv · 2609.14848

Hyperbolicity of renormalization for maps with multiple breaks

Nataliya Goncharuk·Igors Gorbovickis·Michael Yampolsky
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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 $C^{1+α}$-rigidity result for such maps and prove that rigidity classes are analytic submanifolds.

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Nataliya Goncharuk, Igors Gorbovickis, Michael Yampolsky. 2026-09-13. Hyperbolicity of renormalization for maps with multiple breaks. https://arxiv.org/abs/2609.14848

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