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Homoclinic classes of geodesic flows on rank 1 manifolds

Dynamical Systems 2024-09-19 v2 Differential Geometry

Abstract

Given a C1+βC^{1+\beta} flow φ\varphi with positive speed on a closed smooth Riemannian manifold, we code two homoclinically related φ\varphi-invariant probabilities by an irreducible countable topological Markov flow. As an application, we give proofs using symbolic dynamics of the theorem of Knieper on the uniqueness of the measure of maximal entropy and theorems of Burns et al on the uniqueness of equilibrium states.

Keywords

Cite

@article{arxiv.2403.03759,
  title  = {Homoclinic classes of geodesic flows on rank 1 manifolds},
  author = {Yuri Lima and Mauricio Poletti},
  journal= {arXiv preprint arXiv:2403.03759},
  year   = {2024}
}

Comments

10 pages, to appear in Proceedings of the AMS