Uniqueness of the measure of maximal entropy for geodesic flows on certain manifolds without conjugate points

Climenhaga, Vaughn; Knieper, Gerhard; War, Khadim

doi:10.1016/j.aim.2020.107452

Cited by 22 publications

(25 citation statements)

References 36 publications

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“…Burns et al proved the uniqueness of many equilibrium states (including some multiples of the geometric potential and the zero potential) of geodesic flows on rank-one manifolds [BCFT18], and there is a recent preprint that obtains similar results for geodesic flows on surfaces without focal points [CKP20]. There is also a recent preprint that proves the uniqueness of the measure of maximal entropy for geodesic flows on surfaces without conjugate points [CKW19].…”

Section: 1mentioning

confidence: 96%

Symbolic dynamics for non-uniformly hyperbolic systems

Lima¹

2020

Ergod. Th. Dynam. Sys.

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This survey describes the recent advances in the construction of Markov partitions for non-uniformly hyperbolic systems. One important feature of this development comes from a finer theory of non-uniformly hyperbolic systems, which we also describe. The Markov partition defines a symbolic extension that is finite-to-one and onto a non-uniformly hyperbolic locus, and this provides dynamical and statistical consequences such as estimates on the number of closed orbits and properties of equilibrium measures. The class of systems includes diffeomorphisms, flows, and maps with singularities.

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Section: 1mentioning

confidence: 96%

Symbolic dynamics for non-uniformly hyperbolic systems

Lima¹

2020

Ergod. Th. Dynam. Sys.

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“…The uniqueness of MME for manifolds without focal points is obtained in [19]. In [9], the authors proved the uniqueness of MME for the following class H of manifolds without conjugate points that satisfy:…”

Section: Appendix: Manifolds Without Focal/conjugate Pointsmentioning

confidence: 99%

Volume asymptotics and Margulis function in nonpositive curvature

Wu¹

2021

Preprint

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“…It is worth noting that all the assumptions listed above are made at certain prescribed scales. This is particularly useful for certain applications such as the Bonatti-Viana diffeomorphism on T 4 [7], Mañé's derived from Anosov diffeomorphism on T 3 [8], and geodesic flows on surfaces without conjugate points [9]. In many other applications however, Assumption (I) is often replaced by the following, much stronger assumption (see Lemma 2.5):…”

Section: Introductionmentioning

confidence: 99%

Existence and uniqueness of equilibrium states for systems with specification at a fixed scale

Pacífico¹,

Yang²,

Yang³

2022

Preprint

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We consider the uniqueness of equilibrium states for dynamical systems that satisfy certain weak, non-uniform versions of specification, expansivity, and the Bowen property at a fixed scale. Following Climenhaga-Thompson's approach which was originally due to Bowen and Franco, we prove that equilibrium states are unique even when the weak specification assumption only holds on a small collection of orbit segments.

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Uniqueness of the measure of maximal entropy for geodesic flows on certain manifolds without conjugate points

Cited by 22 publications

References 36 publications

Symbolic dynamics for non-uniformly hyperbolic systems

Symbolic dynamics for non-uniformly hyperbolic systems

Volume asymptotics and Margulis function in nonpositive curvature

Existence and uniqueness of equilibrium states for systems with specification at a fixed scale

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