A VECTOR-VALUED ALMOST SURE INVARIANCE PRINCIPLE FOR HYPERBOLIC DYNAMICAL SYSTEMS

• 成果类型: Article
• 署名作者: Melbourne, Ian; Nicol, Matthew
• 署名单位: University of Surrey; University of Houston System; University of Houston
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/08-AOP410
• 发表日期: 2009
• 页码: 478-505
• 关键词: CENTRAL LIMIT-THEOREMS; STATISTICAL PROPERTIES; random-variables; martingales; FLOWS; decay; approximation; recurrence; SEQUENCES; billiards

摘要

We prove an almost sure invariance principle (approximation by d-dimensional Brownian motion) for vector-valued Holder observables of large classes of nonuniformly hyperbolic dynamical systems. These systems include Axiom A diffeomorphisms and flows as well as systems modeled by Young towers with moderate tail decay rates. In particular, the position variable of the planar periodic Lorentz gas with finite horizon approximates a two-dimensional Brownian motion.