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Journal Articles (Review Article) Israel Journal of Mathematics Year : 2020

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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Dates and versions

hal-01737173 , version 1 (19-03-2018)

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Françoise Pène, Benoît Saussol. SPATIO-TEMPORAL POISSON PROCESSES FOR VISITS TO SMALL SETS. Israel Journal of Mathematics, 2020, 240 (2), pp.625-665. ⟨10.1007/s11856-020-2074-0⟩. ⟨hal-01737173⟩
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