Double variational principle for mean dimension
Double variational principle for mean dimension
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DOI：
10.1007/s00039-019-00501-8
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发表时间：
2019-01
影响因子：
2.2
通讯作者：
E. Lindenstrauss;M. Tsukamoto
中科院分区：
文献类型：
--
作者：
E. Lindenstrauss;M. Tsukamoto
We develop a variational principle between mean dimension theory and rate distortion theory. We consider a minimax problem about the rate distortion dimension with respect to two variables (metrics and measures). We prove that the minimax value is equal to the mean dimension for a dynamical system with the marker property. The proof exhibits a new combination of ergodic theory, rate distortion theory and geometric measure theory. Along the way of the proof, we also show that if a dynamical system has the marker property then it has a metric for which the upper metric mean dimension is equal to the mean dimension.
