Almost Sure Invariance Principle For Nonuniformly Hyperbolic Systems
动力系统
2014-12-09 v1
摘要
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.
引用
@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}
}
备注
21 pages, To appear in Communications in Mathematical Physics