Sinai Billiards under Small External Forces II
Sinai Billiards under Small External Forces II
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小外力作用下的西奈台球 II
DOI：
10.1007/s00023-007-0351-7
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发表时间：
2001
期刊：
影响因子：
--
通讯作者：
N. Chernov
中科院分区：
文献类型：
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作者：
N. Chernov
摘要：我们研究了西奈台球的扰动，其中一个小的固定力作用在运动粒子与散射体碰撞之间。在之前的工作 [7] 中，我们证明了碰撞图保留了独特的 Sinai-Ruelle-Bowen (SRB) 测度，即伯努利测度，并且相关性呈指数衰减。在这里，我们添加了其他几个统计属性，包括多重相关的界限、几乎确定不变原理（ASIP）、迭代对数定律和川崎式公式。我们还证明了相应的流是伯努利流并且满足中心极限定理。
Abstract.We study perturbations of Sinai billiards, where a small stationary force acts on the moving particle between its collisions with scatterers. In the previous work [7] we proved that the collision map preserved a unique Sinai–Ruelle–Bowen (SRB) measure that was Bernoulli and had exponential decay of correlations. Here we add several other statistical properties, including bounds on multiple correlations, the almost sure invariance principle (ASIP), the law of iterated logarithms, and a Kawasaki-type formula. We also show that the corresponding flow is Bernoulli and satisfies a central limit theorem.