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

Abstract

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

Minor corrections, short example section added

References in corpus (1)

• Shrinking targets in parametrised families