The ergodic theory of geodesic flows over certain manifolds without conjugate points
Weisheng Wu1
1School of Mathematical Sciences, Xiamen University, Xiamen, 361005, P.R. China
Mathematics Research Reports, Volume 7 (2026), pp. 81-93

In this article, we announce several new results in the ergodic theory of geodesic flows over uniform visibility manifolds without conjugate points. The topics include the ergodicity with respect to the Liouville measure, uniqueness and Bernoulli properties of the measure of maximal entropy and equilibrium states, counting closed geodesics and volume growth asymptotics, Margulis functions and related rigidity phenomenon, and the Hopf-Tsuji-Sullivan dichotomy with respect to the Bowen-Margulis measure. The detailed proof is given in [37].

Received:
Revised:
Published online:
DOI: 10.5802/mrr.29
Classification: 37D40, 37C40
Keywords: Geodesic flows, no conjugate points, Bowen-Margulis measure, equilibrium states, counting closed geodesics, rigidity, Hopf-Tsuji-Sullivan dichotomy

Weisheng Wu  1

1 School of Mathematical Sciences, Xiamen University, Xiamen, 361005, P.R. China
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
Weisheng Wu. The ergodic theory of geodesic flows over certain manifolds without conjugate points. Mathematics Research Reports, Volume 7 (2026), pp. 81-93. doi: 10.5802/mrr.29
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