Exponential Convergence: The Smooth Case

As discussed in Sect. 10.1 , the main motivation behind our study of multicritical circle maps is to understand the smooth rigidity problem. To be more precise, the goal is to answer Question 10.1 : let h be a topological conjugacy between two multicritical circle maps, say f and g, and assume that h identifies each critical point of f with a corresponding critical point of g having the same criticality.