不变熵维的变分原理

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations Pub Date : 2025-10-09 DOI:10.1016/j.jde.2025.113819

Hu Chen , Yu Huang , Xingfu Zhong

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引用次数: 0

摘要

我们引入两种不变性熵维（α-不变性熵），测量理论不变性熵维（测量理论α-不变性熵）和测量理论局部不变性熵维（测量理论局部α-不变性熵）来研究零不变性熵控制系统的复杂性，其中α∈R+。在一定的合理假设下，分别给出了α-不变熵和不变熵维的两种变分原理和反变分原理，并证明了Bowen α-不变熵（Bowen不变熵维）和packing α-不变熵（packing不变熵维）可以通过对应测度的局部熵来确定。

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Variational principles of invariance entropy dimension

We introduce two types of invariance entropy dimensions (α-invariance entropies), measure-theoretic invariance entropy dimensions (measure-theoretic α-invariance entropies), and measure-theoretic local invariance entropy dimensions (measure-theoretic local α-invariance entropy) to investigate the complexity of a control system with zero invariance entropy, where

α \in R_{+}

. Under some reasonable assumptions, we respectively present two variational principles and inverse variational principles for α-invariance entropies and invariance entropy dimensions, and show that Bowen α-invariance entropy (Bowen invariance entropy dimension) and packing α-invariance entropy (packing invariance entropy dimension) can be determined via the corresponding local entropies of measures.

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来源期刊

Journal of Differential Equations 数学-数学

CiteScore

4.40

自引率

8.30%

发文量

543

审稿时长

9 months

期刊介绍： The Journal of Differential Equations is concerned with the theory and the application of differential equations. The articles published are addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations are valuable research tools. Research Areas Include: • Mathematical control theory • Ordinary differential equations • Partial differential equations • Stochastic differential equations • Topological dynamics • Related topics