Lower bounds for the Ruelle spectrum of analytic expanding circle maps

TL;DR

This paper establishes exponential lower bounds for the Ruelle eigenvalues of a dense set of analytic expanding circle maps, using potential theory and explicit spectral calculations.

Contribution

It introduces new lower bounds for Ruelle spectra in analytic expanding circle maps, combining potential theory with explicit spectral analysis of Blaschke products.

Findings

Existence of a dense set of maps with exponential Ruelle eigenvalue bounds

Application of potential theoretic techniques to spectral bounds

Explicit spectral calculations for expanding Blaschke products

Abstract

We prove that there exists a dense set of analytic expanding maps of the circle for which the Ruelle eigenvalues enjoy exponential lower bounds. The proof combines potential theoretic techniques and explicit calculations for the spectrum of expanding Blaschke products.