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Poisson Approximations and Convergence Rates for Hyperbolic Dynamical Systems

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Abstract

We prove the asymptotic functional Poisson laws in the total variation norm and obtain estimates of the corresponding convergence rates for a large class of hyperbolic dynamical systems. These results generalize the ones obtained before in this area. Applications to intermittent solenoids, Axiom A attractors, Hénon attractors and to billiards, are also considered.

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Acknowledgements

We are indebted to I. Melbourne for useful comments and for pointing to the paper [10].

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  1. School of Mathematics, Georgia Institute of Technology, Atlanta, USA

    Yaofeng Su & Leonid A. Bunimovich

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  1. Yaofeng Su
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Correspondence to Yaofeng Su.

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Communicated by C. Liverani.

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Su, Y., Bunimovich, L.A. Poisson Approximations and Convergence Rates for Hyperbolic Dynamical Systems. Commun. Math. Phys. 390, 113–168 (2022). https://doi.org/10.1007/s00220-022-04309-w

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