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

2020/05/04 by Gabriela Estevez, Estevez, Gabriela, Daniel Smania +3
Mathematics · #37E10 #37E20 #37F25 #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Equations Stability Results #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2005.02377

openalex publication_date 2020/05/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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+α rigid.

Related

• Rigidity of analytic and smooth bi-cubic multicritical circle maps with bounded type rotation numbers
• Rigidity of critical circle mappings, II
• Complex bounds for critical circle maps
• Renormalization of bi-cubic circle maps
• Rigidity of critical circle mappings, I