Unique equilibrium states for geodesic flows over surfaces without focal points

Dong Chen, Lien Yung Kao, Kiho Park

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

In this paper, we study dynamics of geodesic flows over closed surfaces of genus greater than or equal to 2 without focal points. Especially, we prove that there is a large class of potentials having unique equilibrium states, including scalar multiples of the geometric potential, provided the scalar is less than 1. Moreover, we discuss ergodic properties of these unique equilibrium states, including the Bernoulli property and the fact that weighted regular periodic orbits are equidistributed relative to these unique equilibrium states.

Original languageEnglish (US)
Pages (from-to)1118-1155
Number of pages38
JournalNonlinearity
Volume33
Issue number3
DOIs
StatePublished - 2020

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

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