Multiple Borel–Cantelli Lemma in dynamics and MultiLog Law for recurrence-Reference-Cited by-同舟云学术

Multiple Borel–Cantelli Lemma in dynamics and MultiLog Law for recurrence

Published:2022 Issue:0 Volume:18 Page:209
ISSN:1930-5311
Container-title:Journal of Modern Dynamics
language:
Short-container-title:JMD

Author:

Dolgopyat Dmitry¹,Fayad Bassam¹,Liu Sixu²

Affiliation:

1. Department of Mathematics, University of Maryland, 4176 Campus Drive, College Park, MD 20742-4015, USA

2. Yau Mathematical Sciences Center, Tsinghua University, Beijing 100084, China

Abstract

<p style='text-indent:20px;'>A classical Borel–Cantelli Lemma gives conditions for deciding whether an infinite number of rare events will happen almost surely. In this article, we propose an extension of Borel–Cantelli Lemma to characterize the multiple occurrence of events on the same time scale. Our results imply multiple Logarithm Laws for recurrence and hitting times, as well as Poisson Limit Laws for systems which are exponentially mixing of all orders. The applications include geodesic flows on compact negatively curved manifolds, geodesic excursions on finite volume hyperbolic manifolds, Diophantine approximations and extreme value theory for dynamical systems.</p>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

Applied Mathematics,Algebra and Number Theory,Analysis,Applied Mathematics,Algebra and Number Theory,Analysis

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