Finite data rigidity for one-dimensional expanding maps
Year: 2024
Type: article
Abstract: Let $f,g$ be $C^2$ 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 $C^2$ conjugacy $h_N$ such that $h_N$ is exponentially close to h in the $C^0$ topology, and $f_N:=h_N^{-1}gh_N$ is exponentially close to f in the $C^1$ topology. Our main tool is a uniform effective version of Bowen’s equidistribution of weighted periodic orbits to the equilibrium state.
DOI: 10.1017/etds.2024.83
Author: THOMAS ALOYSIUS O’HARE
Institution: The Ohio State University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,450
OpenAlex ID: W4404329663