A footnote on Expanding maps

TL;DR

This paper introduces Banach spaces tailored for analyzing the spectrum of transfer operators linked to piecewise expanding maps with Hölder weights, enabling precise spectral characterization.

Contribution

It presents a novel Banach space framework that allows exact spectral analysis of transfer operators for certain expanding maps.

Findings

Spectral properties of transfer operators are precisely characterized.

The framework applies to maps with Hölder continuous weights.

Enhanced understanding of dynamical systems' spectral behavior.

Abstract

I introduce Banach spaces on which it is possible to precisely characterize the spectrum of the transfer operator associated to a piecewise expanding map with H\"older weight.