Equilibrium measures of manifolds without conjugate points having visibility covering
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911296254902272 |
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| author | Mamani, Edhin |
| author_facet | Mamani, Edhin |
| contents | In this paper we study the equilibrium measures of geodesic flows of closed manifolds without conjugate points which have a visibility universal covering. Specifically, the uniqueness problem for Bowen potentials which are constants on some sets--intersection of horospheres-- and satisfy a weak pressure gap. Moreover, we study some ergodic properties of these measures such as the K-mixing property, weighted equidistribution of closed geodesics, the Gibbs property, large deviations and the entropy density of ergodic measures. Assuming, furthermore continuity of Green bundles, existence of a hyperbolic closed geodesic and a Gromov hyperbolic universal covering we prove that the above potentials always satisfy the weak pressure gap. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_01290 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Equilibrium measures of manifolds without conjugate points having visibility covering Mamani, Edhin Dynamical Systems Differential Geometry In this paper we study the equilibrium measures of geodesic flows of closed manifolds without conjugate points which have a visibility universal covering. Specifically, the uniqueness problem for Bowen potentials which are constants on some sets--intersection of horospheres-- and satisfy a weak pressure gap. Moreover, we study some ergodic properties of these measures such as the K-mixing property, weighted equidistribution of closed geodesics, the Gibbs property, large deviations and the entropy density of ergodic measures. Assuming, furthermore continuity of Green bundles, existence of a hyperbolic closed geodesic and a Gromov hyperbolic universal covering we prove that the above potentials always satisfy the weak pressure gap. |
| title | Equilibrium measures of manifolds without conjugate points having visibility covering |
| topic | Dynamical Systems Differential Geometry |
| url | https://arxiv.org/abs/2512.01290 |