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Journal of Statistical Physics

, Volume 172, Issue 6, pp 1499–1524 | Cite as

Non-stationary Almost Sure Invariance Principle for Hyperbolic Systems with Singularities

  • Jianyu ChenEmail author
  • Yun Yang
  • Hong-Kun Zhang
Article

Abstract

We investigate a wide class of two-dimensional hyperbolic systems with singularities, and prove the almost sure invariance principle (ASIP) for the random process generated by sequences of dynamically Hölder observables. The observables could be unbounded, and the process may be non-stationary and need not have linearly growing variances. Our results apply to Anosov diffeomorphisms, Sinai dispersing billiards and their perturbations. The random processes under consideration are related to the fluctuation of Lyapunov exponents, the shrinking target problem, etc.

Keywords

ASIP Non-stationarity Hyperbolicity Singularities 

Mathematics Subject Classification

37D50 37A25 60F17 

Notes

Acknowledgements

The authors would like to thank Nicolai Haydn and Huyi Hu for helpful discussions and suggestions.

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Copyright information

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Authors and Affiliations

  1. 1.Department of Mathematics & StatisticsUniversity of Massachusetts AmherstAmherstUSA
  2. 2.Mathematics Department, The Graduate CenterCity University of New YorkNew YorkUSA

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