Measure-theoretic metric mean dimension
Rui Yang, Ercai Chen, Xiaoyao Zhou

TL;DR
This paper introduces a new measure-theoretic metric mean dimension concept for infinite entropy systems, linking it to packing mean dimension of generic points, advancing understanding of complex dynamical systems.
Contribution
It defines measure-theoretic metric mean dimension for infinite entropy systems and establishes its equivalence with packing mean dimension of generic points.
Findings
Measure-theoretic metric mean dimensions coincide across different types of measure-theoretic ε-entropies.
The measure-theoretic metric mean dimension equals the packing metric mean dimension of generic points.
Provides a new framework for analyzing infinite measure-theoretic entropy systems.
Abstract
For infinite measure-theoretic entropy systems, we introduce the notion of measure-theoretic metric mean dimension of invariant measures for different types of measure-theoretic -entropies, and show that measure-theoretic metric mean dimensions of different types of measure-theoretic -entropies coincide with the packing metric mean dimension of the set of generic points of ergodic measures.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Computability, Logic, AI Algorithms · Advanced Thermodynamics and Statistical Mechanics
