Double variational principle for mean dimension with potential
Double variational principle for mean dimension with potential
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DOI：
10.1016/j.aim.2019.106935
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发表时间：
2019-01
期刊：
影响因子：
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通讯作者：
M. Tsukamoto
中科院分区：
文献类型：
--
作者：
M. Tsukamoto
本文对动力系统的平均维理论作出了贡献。我们引入了具有位势的平均维的概念，并发展了它的变分原理。这是拓扑压力理论的一个平均维度类比。我们考虑了一个率失真维度与势函数积分之和的极大极小问题。证明了具有标记性的动力系统的极小极大值等于具有位势的平均维。证明的基本思想是几何测度论的动态化。
This paper contributes to the mean dimension theory of dynamical systems. We introduce a new concept called mean dimension with potential and develop a variational principle for it. This is a mean dimension analogue of the theory of topological pressure. We consider a minimax problem for the sum of rate distortion dimension and the integral of a potential function. We prove that the minimax value is equal to the mean dimension with potential for a dynamical system having the marker property. The basic idea of the proof is a dynamicalization of geometric measure theory.