Anisotropic spaces for the bilateral shift

Fuente: arXiv
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Autori principali: Marra, Mateus, Smania, Daniel
Natura: Preprint
Pubblicazione: 2024
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author Marra, Mateus
Smania, Daniel
author_facet Marra, Mateus
Smania, Daniel
contents Given two Hölder potentials $ϕ_+$ and $ψ_-$ for the unilateral shift, we define anisotropic Banach spaces of distributions on the bilateral shift space with a finite alphabet. On these spaces, the transfer operator for the bilateral shift is quasicompact with a spectral gap, and the unique Gibbs state associated with $ϕ_+$ spans its $1$-eigenspace. This result allows us to establish exponential decay of correlations for Hölder observables and a wide range of measures on the bilateral shift space.
format Preprint
id arxiv_https___arxiv_org_abs_2411_15050
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Anisotropic spaces for the bilateral shift
Marra, Mateus
Smania, Daniel
Dynamical Systems
Analysis of PDEs
Functional Analysis
37A25, 37A30, 37A46, 37C30, 37D05, 37D35, 37D20, 43A85, 47B37, 43A15, 46E36, 46F99
Given two Hölder potentials $ϕ_+$ and $ψ_-$ for the unilateral shift, we define anisotropic Banach spaces of distributions on the bilateral shift space with a finite alphabet. On these spaces, the transfer operator for the bilateral shift is quasicompact with a spectral gap, and the unique Gibbs state associated with $ϕ_+$ spans its $1$-eigenspace. This result allows us to establish exponential decay of correlations for Hölder observables and a wide range of measures on the bilateral shift space.
title Anisotropic spaces for the bilateral shift
topic Dynamical Systems
Analysis of PDEs
Functional Analysis
37A25, 37A30, 37A46, 37C30, 37D05, 37D35, 37D20, 43A85, 47B37, 43A15, 46E36, 46F99
url https://arxiv.org/abs/2411.15050