SRB Measures and Young Towers for Surface Diffeomorphisms

Climenhaga, Vaughn; Luzzatto, Stefano; Pesin, Yakov

doi:10.1007/s00023-021-01113-5

Cited by 4 publications

(2 citation statements)

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“…Estimate R 2 . To estimate R 2 , we first note that since {Z 0 ≥ 1} ∈ σ(A n+2K+1 ), and n will be sent to infinity while K is fixed 9 , one cannot use the mixing assumption on P (Z 0 ≥ 1 ∧ Z j ≥ 1) for small values of j.…”

Section: 1mentioning

confidence: 99%

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Rare event process and entry times distribution for arbitrary null sets on compact manifolds

Yang

2019

Preprint

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We establish the general equivalence between rare event process for arbitrary continuous functions whose maximal values are achieved on nontrivial sets, and the entry times distribution for arbitrary measure zero sets. We then use it to show that the for differentiable maps on a compact Riemannian manifold that can be modeled by Young's towers, the rare event process and the limiting entry times distribution both converge to compound Poisson distributions. A similar result is also obtained on Gibbs-Markov systems, for both cylinders and open sets. We also give explicit expressions for the parameters of the limiting distribution, and a simple criterion for the limiting distribution to be Poisson. This can be applied to a large family of continuous observables that achieve their maximum on a non-trivial set with zero measure.

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Section: 1mentioning

confidence: 99%

“…In the case of C 1+α surface diffeomorphisms, one can always construct towers using the first return map. See[9, Theorem B] …”

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confidence: 99%