Transfer operators and atomic decomposition

Autor: Arbieto, Alexander, Smania, Daniel
Rok vydání: 2019
Předmět:
Druh dokumentu: Working Paper
Popis: 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.
Comment: 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
Databáze: arXiv