具有近似积性质的动力系统中间熵的遍历测度

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics Pub Date : 2025-02-18 DOI:10.1016/j.aim.2025.110159

Peng Sun

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引用次数: 0

摘要

对于满足近似积性质和渐近熵扩张性的动力系统，我们刻画了不变测度空间的一个精细结构：中间熵的遍历测度和中间压力的遍历测度在某些子空间中是一般的。因此，对于一类广泛的系统，证明了Katok关于存在任意中间熵的遍历测度的猜想。

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Ergodic measures of intermediate entropies for dynamical systems with the approximate product property

For a dynamical system satisfying the approximate product property and asymptotically entropy expansiveness, we characterize a delicate structure of the space of invariant measures: The ergodic measures of intermediate entropies and the ones of intermediate pressures are generic in certain subspaces. Consequently, the conjecture of Katok that ergodic measures of arbitrary intermediate entropy exist is verified for a broad class of systems.

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来源期刊

Advances in Mathematics 数学-数学

CiteScore

2.80

自引率

5.90%

发文量

497

审稿时长

7.5 months

期刊介绍： Emphasizing contributions that represent significant advances in all areas of pure mathematics, Advances in Mathematics provides research mathematicians with an effective medium for communicating important recent developments in their areas of specialization to colleagues and to scientists in related disciplines.