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Mathematics > Dynamical Systems

arXiv:1804.09708 (math)
[Submitted on 25 Apr 2018]

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

Authors:Jianyu Chen, Hongkun Zhang, Yun Yang
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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.
Subjects: Dynamical Systems (math.DS)
Cite as: arXiv:1804.09708 [math.DS]
  (or arXiv:1804.09708v1 [math.DS] for this version)
  https://doi.org/10.48550/arXiv.1804.09708
Related DOI: https://doi.org/10.1007/s10955-018-2107-9

Submission history

From: Yun Yang [view email]
[v1] Wed, 25 Apr 2018 17:56:12 UTC (25 KB)
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