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A recurrence-type strong Borel-Cantelli lemma for Axiom A diffeomorphisms

Rodriguez Sponheimer, Alejandro LU (2025) In Ergodic Theory and Dynamical Systems 45(3). p.936-955
Abstract

Let (X, μ, T , d) be a metric measure-preserving dynamical system such that three-fold correlations decay exponentially for Lipschitz continuous observables. Given a sequence (Mk) that converges to 0 slowly enough, we obtain a strong dynamical Borel.Cantelli result for recurrence, that is, for μ-almost every x ∈ X, {equation presented} where μ(Bk(x)) = Mk. In particular, we show that this result holds for Axiom A diffeomorphisms and equilibrium states under certain assumptions.

Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Axiom A diffeomorphisms, recurrence, strong Borel-Cantelli lemma
in
Ergodic Theory and Dynamical Systems
volume
45
issue
3
pages
20 pages
publisher
Cambridge University Press
external identifiers
  • scopus:85204532545
ISSN
0143-3857
DOI
10.1017/etds.2024.64
language
English
LU publication?
yes
id
2f16b5c2-3bb7-4dca-ab20-22ea92406418
date added to LUP
2024-11-27 13:07:04
date last changed
2025-05-23 17:31:22
@article{2f16b5c2-3bb7-4dca-ab20-22ea92406418,
  abstract     = {{<p>Let (X, μ, T , d) be a metric measure-preserving dynamical system such that three-fold correlations decay exponentially for Lipschitz continuous observables. Given a sequence (M<sub>k</sub>) that converges to 0 slowly enough, we obtain a strong dynamical Borel.Cantelli result for recurrence, that is, for μ-almost every x ∈ X, {equation presented} where μ(B<sub>k</sub>(x)) = M<sub>k</sub>. In particular, we show that this result holds for Axiom A diffeomorphisms and equilibrium states under certain assumptions.</p>}},
  author       = {{Rodriguez Sponheimer, Alejandro}},
  issn         = {{0143-3857}},
  keywords     = {{Axiom A diffeomorphisms; recurrence; strong Borel-Cantelli lemma}},
  language     = {{eng}},
  number       = {{3}},
  pages        = {{936--955}},
  publisher    = {{Cambridge University Press}},
  series       = {{Ergodic Theory and Dynamical Systems}},
  title        = {{A recurrence-type strong Borel-Cantelli lemma for Axiom A diffeomorphisms}},
  url          = {{http://dx.doi.org/10.1017/etds.2024.64}},
  doi          = {{10.1017/etds.2024.64}},
  volume       = {{45}},
  year         = {{2025}},
}