当前位置: X-MOL 学术Stoch. Dyn. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Generic properties of invariant measures of full-shift systems over perfect Polish metric spaces
Stochastics and Dynamics ( IF 1.1 ) Pub Date : 2021-01-09 , DOI: 10.1142/s0219493721500404
Silas L. Carvalho 1 , Alexander Condori 2
Affiliation  

In this work, we are interested in characterizing typical (generic) dimensional properties of invariant measures associated with the full-shift system, T, in a product space whose alphabet is a perfect Polish metric space (thus, uncountable). More specifically, we show that the set of invariant measures with upper Hausdorff dimension equal to zero and lower packing dimension equal to infinity is a dense Gδ subset of (T), the space of T-invariant measures endowed with the weak topology. We also show that the set of invariant measures with upper rate of recurrence equal to infinity and lower rate of recurrence equal to zero is a Gδ subset of (T). Furthermore, we show that the set of invariant measures with upper quantitative waiting time indicator equal to infinity and lower quantitative waiting time indicator equal to zero is residual in (T).

中文翻译:

完美波兰度量空间上全移位系统不变测度的一般性质

在这项工作中,我们感兴趣的是表征与全班制系统相关的不变测量的典型(通用)维度属性,,在其字母表是完美波兰度量空间(因此,不可数)的乘积空间中。更具体地说,我们证明了上 Hausdorff 维数等于 0 且下包装维数等于无穷大的不变测度集是稠密的Gδ的子集(), 的空间- 具有弱拓扑的不变测度。我们还表明,上限复发率等于无穷大且下限复发率等于零的一组不变测度是Gδ的子集(). 此外,我们表明,上定量等待时间指标等于无穷大和下定量等待时间指标等于零的一组不变测度在().
更新日期:2021-01-09
down
wechat
bug