论文标题
分散台球图的最大熵的混合速率
Rates of mixing for the measure of maximal entropy of dispersing billiard maps
论文作者
论文摘要
在最近的一项工作中，Baladi和Demers构建了有限地平线分散台球地图的最大熵的度量，并证明了它是独特的，混合的，而且是Bernoulli。我们表明，该措施具有Hölder连续可观察物的天然概率特性，例如至少相关性的多项式衰减和中心极限定理。 Baladi和Demers的结果受到奇异性稀疏复发的条件。我们使用类似且稍强的条件，它对我们的相关性衰减率有直接影响。对于具有有界复杂性的台球表（一种属性是通用的属性），我们表明稀疏的复发条件总是满足，并且相关性衰减以超多项式率。
In a recent work, Baladi and Demers constructed a measure of maximal entropy for finite horizon dispersing billiard maps and proved that it is unique, mixing and moreover Bernoulli. We show that this measure enjoys natural probabilistic properties for Hölder continuous observables, such as at least polynomial decay of correlations and the Central Limit Theorem. The results of Baladi and Demers are subject to a condition of sparse recurrence to singularities. We use a similar and slightly stronger condition, and it has a direct effect on our rate of decay of correlations. For billiard tables with bounded complexity (a property conjectured to be generic), we show that the sparse recurrence condition is always satisfied and the correlations decay at a super-polynomial rate.
