Finite Data Rigidity for One-Dimensional Expanding Maps

2023/10/30 by O'Hare, Thomas · 2 citations
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2310.20027

Abstract

Let f,g be C² expanding maps on the circle which are topologically conjugate. We assume that the derivatives of f and g at corresponding periodic points coincide for some large period N. We show that f and g are "approximately smoothly conjugate." Namely, we construct a C² conjugacy h_N such that h_N is exponentially close to h in the C⁰ topology, and f_N:=h_N^-1gh_N is exponentially close to f in the C¹ topology. Our main tool is a uniform effective version of Bowen's equidistribution of weighted periodic orbits to the equilibrium state.

Cited by

• Effective Equidistribution for Contact Anosov flows in Dimension Three
• Unmarked spectral rigidity of expanding circle maps

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