Ergodic optimization theory for a class of typical maps
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 C^{0, \alpha} with \alpha\in(0,1] or C^{1} (if well defined), the optimal (minimizing or maximizing) orbits are generically periodic, thus confirming the conjecture in those cases.
Authors
- Xiao Ma (ORCID: https://orcid.org/0000-0002-1083-4063)
- Yiwei Zhang (ORCID: https://orcid.org/0000-0002-3499-9911)
- Wen Huang (ORCID: https://orcid.org/0000-0002-7673-9624)
- Zeng Lian (ORCID: https://orcid.org/0000-0003-3505-1468)
- Leiye Xu (ORCID: https://orcid.org/0000-0002-5389-1690)
Institutions
- University of Science and Technology of China (CN)
- Anhui University of Science and Technology (CN)
- Sichuan University (CN)
- Southern University of Science and Technology (CN)
Publication Details
- Journal
- Journal of the European Mathematical Society
- Published
- 2025-06-17
- DOI
- https://doi.org/10.4171/jems/1652
- Citations
- 4
- Primary Topic
- Advanced Differential Equations and Dynamical Systems
- Type
- article
- Field-Weighted Citation Impact
- 16.35