Large deviations estimates for dynamical systems without the specification property. Application to the β-shifts
Large deviations estimates for dynamical systems without the specification property. Application to the β-shifts
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DOI：
10.1088/0951-7715/18/1/013
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发表时间：
2004
期刊：
影响因子：
1.7
通讯作者：
C-E Pfister;W G Sullivan
中科院分区：
文献类型：
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作者：
C-E Pfister;W G Sullivan
我们考虑动力系统的轨道集验证一个近似的产品属性。这使我们能够获得大的偏差结果，这是以前证明的条件下的规格属性。我们通过考虑β位移来说明我们的结果。当指定性质对勒贝格测度为零的β > 1的集合成立时，我们的近似乘积性质对任何β > 1成立。对于任意的β位移，经验测度证明了关于最大熵概率测度的大偏差原理。我们将Pfister和Sullivan（2003 Nonlinearity 16 661-82）的维数结果推广到任意β-移位，得到了包含遍历平均的集合的拓扑熵的变分原理.
We consider dynamical systems whose sets of orbits verify an approximate product property. This allows us to obtain large deviations results, which were previously proven under the condition of specification property. We illustrate our results by considering the β-shifts. While the specification property holds for a set of β > 1 of Lebesgue measure zero, our approximate product property holds for any β > 1. For any β-shift the empirical measures verify a large deviations principle with respect to the probability measure of maximal entropy. We extend the dimension results of Pfister and Sullivan (2003 Nonlinearity 16 661–82) to any β-shift, obtaining a variational principle for the topological entropy of sets involving ergodic averages.