C¹ Robust Rigidity for Bi-critical Circle Maps

2025/01/10 by Estevez, Gabriela
#37E10 #37E20 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2501.06329

Abstract

We prove that two topologically conjugate bi-critical circle maps whose signatures are the same, and whose renormalizations converge together exponentially fast in the C²-topology, are C¹ conjugate.

Related

• Rigidity of critical circle mappings, I
• Rigidity of critical circle mappings, II
• The rigidity problem for analytic critical circle maps
• Rigidity of analytic and smooth bi-cubic multicritical circle maps with bounded type rotation numbers
• Real bounds and quasisymmetric rigidity of multicritical circle maps