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arXiv 1901.05628math.DScs.ITmath.IT
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位势平均维数的二重变分原理

Double variational principle for mean dimension with potential

Masaki Tsukamoto

摘要:

本文对动力系统的平均维数论作出了贡献。本文引入了一个新的概念--平均位势维数,并建立了它的变分原理,这是平均位势维数与拓扑压理论的一个类比。我们考虑一个率失真维数与一个势函数的积分之和的极大极小问题。证明了具有标记性质的动力系统的极大极小值等于其位势的平均维数。证明的基本思想是几何测度论的动态化。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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