Complex a priori bounds for multicritical circle maps with bounded type rotation number

Abstract

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 $C^{1+\alpha }$ rigid.

15 pages, 6 figures. arXiv admin note: text overlap with arXiv:1909.01451

References in corpus (1)

• Renormalization of bicritical circle maps

Cited by in corpus (1)

• Automorphic measures and invariant distributions for circle dynamics