The Dolgopyat inequality in \BV\ for non-Markov maps

TL;DR

This paper establishes the Dolgopyat inequality for transfer operators associated with non-Markov, piecewise expanding interval maps acting on BV space, extending key spectral gap results to a broader class of dynamical systems.

Contribution

It proves the Dolgopyat inequality for twisted transfer operators of non-Markov maps on BV space, generalizing previous results to more complex dynamical systems.

Findings

Dolgopyat inequality holds for non-Markov maps on BV space

Spectral gap properties are established for the transfer operator

Results extend to systems with piecewise $C^1$ roof functions

Abstract

Let $F$ be a (non-Markov) countably piecewise expanding interval map satisfying certain regularity conditions, and $\tilde\L$ the corresponding transfer operator. We prove the Dolgopyat inequality for the twisted operator $\tilde\L_s(v) = \tilde\L_s(e^{s\varphi}v)$ acting on the space BV of functions of bounded variation, where $\varphi$ is a piecewise $C^1$ roof function.