The rigidity problem for analytic critical circle maps

2005/01/25 by Khmelev, D., Yampolsky, M.
#37E10 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0501448

Abstract

It is shown that if f and g are any two analytic critical circle mappings with the same irrational rotation number, then the conjugacy that maps the critical point of f to that of g has regularity C^1+α at the critical point, with a universal value of α>0. As a consequence, a new proof of the hyperbolicity of the full renormalization horseshoe of critical circle maps is given.

Related

• Rigidity of critical circle mappings, II
• Rigidity of critical circle mappings, I
• Rigidity, universality,and hyperbolicity of renormalization for critical circle maps with non-integer exponents
• Renormalization of unicritical analytic circle maps
• Rigidity of analytic and smooth bi-cubic multicritical circle maps with bounded type rotation numbers