Poisson Approximations and Convergence Rates for Hyperbolic Dynamical Systems

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 a...

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Bibliographic Details
Published in:	Communications in mathematical physics Vol. 390; no. 1; pp. 113 - 168
Main Authors:	Su, Yaofeng, Bunimovich, Leonid A.
Format:	Journal Article
Language:	English
Published:	Berlin/Heidelberg Springer Berlin Heidelberg 01-02-2022 Springer Nature B.V
Subjects:	Attractors (mathematics) Classical and Quantum Gravitation Complex Systems Convergence Dynamical systems Mathematical and Computational Physics Mathematical Physics Physics Physics and Astronomy Quantum Physics Relativity Theory Solenoids Theoretical
Online Access:	Get full text
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Summary:	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.
ISSN:	0010-3616 1432-0916
DOI:	10.1007/s00220-022-04309-w