A VECTOR-VALUED ALMOST SURE INVARIANCE PRINCIPLE FOR HYPERBOLIC DYNAMICAL SYSTEMS
A VECTOR-VALUED ALMOST SURE INVARIANCE PRINCIPLE FOR HYPERBOLIC DYNAMICAL SYSTEMS
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DOI：
10.1214/08-aop410
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发表时间：
2009-03-01
影响因子：
2.3
通讯作者：
Nicol, Matthew
中科院分区：
文献类型：
--
作者：
Melbourne, Ian;Nicol, Matthew
证明了一大类非一致双曲动力系统的向量值Holder可观测量的几乎必然不变性原理(用d维布朗运动逼近)。这些系统包括公理A微分同胚和流，以及由Young Tower模拟的具有中等尾部衰减率的系统。特别是，有限视界平面周期Lorentz气体的位置变量近似为二维布朗运动。
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.