Rigidity of analytic and smooth bi-cubic multicritical circle maps with bounded type rotation numbers

2021/12/10 by Igors Gorbovickis, Gorbovickis, Igors, Michael Yampolsky +1
Mathematics · Computer Science · Physics and Astronomy · #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2112.05845

Abstract

We prove that if two analytic multicritical circle maps with the same bounded type rotation number are topologically conjugate by a conjugacy which matches the critical points of the two maps while preserving the orders of their criticalities, then the conjugacy necessarily has C^1+α regularity, where α depends only on the bound on the type of the rotation number. We then extend this rigidity result to C³-smooth bi-cubic circle maps.

Related

• Rigidity of critical circle mappings, II
• Complex a priori bounds for multicritical circle maps with bounded type rotation number
• Rigidity of critical circle mappings, I
• The rigidity problem for analytic critical circle maps
• C¹ Robust Rigidity for Bi-critical Circle Maps