Transfer operators and atomic decomposition
Dynamical Systems
2020-09-03 v3 Classical Analysis and ODEs
Functional Analysis
Abstract
We use the method of atomic decomposition and a new family of Banach spaces to study the action of transfer operators associated to piecewise-defined maps. It turns out that these transfer operators are quasi-compact even when the associated potential, the dynamics and the underlying phase space have very low regularity. In particular it is often possible to obtain exponential decay of correlations, the Central Limit Theorem and almost sure invariance principle for fairly general observables, including unbounded ones.
Cite
@article{arxiv.1903.06943,
title = {Transfer operators and atomic decomposition},
author = {Alexander Arbieto and Daniel Smania},
journal= {arXiv preprint arXiv:1903.06943},
year = {2020}
}
Comments
46 pages, 2 figures. We fixed a few typos, updated the bibliography and we also included complete proofs of Theorem 15.1, Corollary 15.1 and 15.2