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SPATIO-TEMPORAL POISSON PROCESSES FOR VISITS TO SMALL SETS

Abstract : For many measure preserving dynamical systems (Ω, T, m) the successive hitting times to a small set is well approximated by a Poisson process on the real line. In this work we define a new process obtained from recording not only the successive times n of visits to a set A, but also the position T n (x) in A of the orbit, in the limit where m(A) → 0. We obtain a convergence of this process, suitably normalized, to a Poisson point process in time and space under some decorrelation condition. We present several new applications to hyperbolic maps and SRB measures, including the case of a neighborhood of a periodic point, and some billiards such as Sinai billiards, Bunimovich stadium and diamond billiard.
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https://hal.univ-brest.fr/hal-01737173
Contributor : Benoit Saussol <>
Submitted on : Monday, March 19, 2018 - 12:03:50 PM
Last modification on : Wednesday, April 1, 2020 - 1:57:16 AM
Long-term archiving on: : Tuesday, September 11, 2018 - 7:36:24 AM

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  • HAL Id : hal-01737173, version 1

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Françoise Pène, Benoit Saussol. SPATIO-TEMPORAL POISSON PROCESSES FOR VISITS TO SMALL SETS. 2018. ⟨hal-01737173⟩

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