Renormalization of Analytic Multicritical Circle Maps with Bounded Type Rotation Numbers

Gabriela Estevez,Daniel Smania,Michael Yampolsky

Bulletin of the Brazilian Mathematical Society, New Series（2022）

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摘要

In this paper, we study homeomorphisms of the circle with several critical points and bounded type rotation number. We prove complex a priori bounds for these maps. As an application, we get that bi-cubic circle maps with same bounded type rotation number are C^1+α rigid.

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关键词

Renormalization, Multicritical critical circle maps, Complex bounds, Real bounds, Rigidity, Primary 37E10 Secondary 37E20, 37F25

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