Decay of correlations for slowly mixing flows
Decay of correlations for slowly mixing flows
复制标题
DOI：
10.1112/plms/pdn028
复制
发表时间：
2006-11
影响因子：
1.8
通讯作者：
I. Melbourne
中科院分区：
文献类型：
--
作者：
I. Melbourne
我们发现多项式衰减的相关性是普遍的一类非均匀双曲流。这些流量是连续时间模拟一类非一致双曲型的同构，其中杨证明多项式衰减的相关性。粗略地说，在之前已经证明了非同态的衰减率<$（1/nβ）的情况下，我们建立了流的衰减率<$（1/tβ）。应用包括某些类别的半分散台球，以及分散台球与消失曲率。此外，我们得到的结果与无界屋顶功能的悬浮流。特别是，经典的平面洛伦兹流与双周期阵列的圆形散射体的衰减率为1/t的物理学家所预期的。
We show that polynomial decay of correlations is prevalent for a class of nonuniformly hyperbolic flows. These flows are the continuous time analogue of a class of nonuniformly hyperbolic diffeomorphisms for which Young proved polynomial decay of correlations. Roughly speaking, in situations where the decay rate 𝒪(1/nβ) has previously been proved for diffeomorphisms, we establish the decay rate 𝒪(1/tβ) for flows. Applications include certain classes of semidispersing billiards, as well as dispersing billiards with vanishing curvature. In addition, we obtain results for suspension flows with unbounded roof functions. In particular, the classical planar Lorentz flow with a doubly periodic array of circular scatterers has decay rate 1/t as anticipated by physicists.