Almost Sure Invariance Principle For Nonuniformly Hyperbolic Systems
Dynamical Systems
2014-12-09 v1
Abstract
We prove an almost sure invariance principle that is valid for general classes of nonuniformly expanding and nonuniformly hyperbolic dynamical systems. Discrete time systems and flows are covered by this result. In particular, the result applies to the planar periodic Lorentz flow with finite horizon. Statistical limit laws such as the central limit theorem, the law of the iterated logarithm, and their functional versions, are immediate consequences.
Keywords
Cite
@article{arxiv.math/0503693,
title = {Almost Sure Invariance Principle For Nonuniformly Hyperbolic Systems},
author = {Ian Melbourne and Matthew Nicol},
journal= {arXiv preprint arXiv:math/0503693},
year = {2014}
}
Comments
21 pages, To appear in Communications in Mathematical Physics