On the prevalence of the periodicity of maximizing measures

Ding，Jian1; Li，Zhiqiang2; Zhang，Yiwei3

2024-02-01

10.1016/j.aim.2023.109485

Advances in Mathematics   影响因子和分区

0001-8708

1090-2082

For a continuous map T:X→X on a compact metric space (X,d), we say that a function f:X→R has the property P if its time averages along forward orbits of T are maximized at a periodic orbit. In this paper, we prove that for the one-sided full shift on two symbols, the property P is prevalent (in the sense of Hunt–Sauer–Yorke) in spaces of Lipschitz functions with respect to metrics with mildly fast decaying rate on the diameters of cylinder sets. This result is a strengthening of [3, Theorem A], confirms the prediction mentioned in the ICM proceeding contribution of J. Bochi ([1, Section 1]) suggested by experimental evidence, and is another step towards the Hunt–Ott conjectures in the area of ergodic optimization.

(Random) maximum mean cycle Ergodic optimization Ground state Maximizing measure Prevalence

SCI

英语

其他

MATHEMATICS

2-s2.0-85182004918

Scopus

1.School of Mathematical Sciences,Peking University,Beijing,100871,China
2.School of Mathematical Sciences,Beijing International Center for Mathematical Research,Peking University,Beijing,100871,China
3.Department of Mathematics,SUSTech International Center for Mathematics,Southern University of Science and Technology,Shenzhen,Guangdong,518055,China

Ding，Jian,Li，Zhiqiang,Zhang，Yiwei. On the prevalence of the periodicity of maximizing measures[J]. Advances in Mathematics,2024,438.

Ding，Jian,Li，Zhiqiang,&Zhang，Yiwei.(2024).On the prevalence of the periodicity of maximizing measures.Advances in Mathematics,438.

Ding，Jian,et al."On the prevalence of the periodicity of maximizing measures".Advances in Mathematics 438(2024).