Parameter regularity of dynamical determinants of expanding maps of the circle and an application to linear response

TL;DR

This paper establishes the regularity of dynamical determinants for expanding circle maps, extending linear response formulas from analytic to differentiable settings using transfer operator decomposition.

Contribution

It introduces a novel approach to prove regularity of dynamical determinants in the differentiable setting, adapting previous analytic results.

Findings

Proves regularity of dynamical determinants for expanding circle maps.

Extends linear response formulas to differentiable maps.

Uses transfer operator decomposition into nuclear and bounded parts.

Abstract

In order to adapt to the differentiable setting a formula for linear response proved by Pollicott and Vytnova in the analytic setting, we show a result of regularity of dynamical determinants of expanding maps of the circle. The main tool is the decomposition of a transfer operator as a sum of a nuclear part and a "small" bounded part.