Non-stationary Almost Sure Invariance Principle for Hyperbolic Systems with Singularities
arXiv:1804.09708 · doi:10.1007/s10955-018-2107-9
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.
References in corpus (10)
- Ruelle-Perron-Frobenius spectrum for Anosov maps
- Almost Sure Invariance Principle For Nonuniformly Hyperbolic Systems
- Strong invariance principles for dependent random variables
- Billiards with polynomial mixing rates
- Almost sure invariance principle for dynamical systems by spectral methods
- Limit theorems in the stadium billiard
- A functional analytic approach to perturbations of the Lorentz gas
- Dispersing billiards with moving scatterers
- Equidistribution for nonuniformly expanding dynamical systems, and application to the almost sure invariance principle
- Central limit theorems for the shrinking target problem