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Ergodic optimization theory for a class of typical maps

  • Wen Huang

    University of Science and Technology of China, Hefei, P. R. China

  • Zeng Lian

    Sichuan University, Chengdu, P. R. China

  • Xiao Ma

    University of Science and Technology of China, Hefei, P. R. China
    ORCID

  • Leiye Xu

    University of Science and Technology of China, Hefei, P. R. China

  • Yiwei Zhang

    Anhui University of Science and Technology, Huainan, P. R. China; Southern University of Science and Technology, Shenzhen, P. R. China
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Abstract

We study the ergodic optimization problem for a class of typical maps including Axiom A attractors, Anosov diffeomorphisms, subshifts of finite type and uniformly expanding systems. In connection with the conjecture proposed by Yuan and Hunt in 1999, we prove that when the space of observables is with or (if well defined), the optimal (minimizing or maximizing) orbits are generically periodic, thus confirming the conjecture in those cases.

Cite this article

Wen Huang, Zeng Lian, Xiao Ma, Leiye Xu, Yiwei Zhang, Ergodic optimization theory for a class of typical maps. J. Eur. Math. Soc. (2025), published online first

DOI 10.4171/JEMS/1652