Equilibrium measures for some partially hyperbolic systems
We study thermodynamic formalism for topologically transitive partially hyperbolic systems in
which the center-stable bundle satisfies a bounded expansion property, and show that every …
which the center-stable bundle satisfies a bounded expansion property, and show that every …
Existence and uniqueness of equilibrium states for systems with specification at a fixed scale: an improved Climenhaga–Thompson criterion
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 …
weak, non-uniform versions of specification, expansivity, and the Bowen property at a fixed …
Unique equilibrium states for Bonatti–Viana diffeomorphisms
We show that the robustly transitive diffeomorphisms constructed by Bonatti and Viana have
unique equilibrium states for natural classes of potentials. In particular, we characterize the …
unique equilibrium states for natural classes of potentials. In particular, we characterize the …
Equilibrium states for self‐products of flows and the mixing properties of rank 1 geodesic flows
B Call, DJ Thompson - Journal of the London Mathematical …, 2022 - Wiley Online Library
Equilibrium states for geodesic flows over closed rank 1 manifolds were studied recently in
Burns, Climenhaga, Fisher, and Thompson [Geom. Funct. Anal. 28 (2018), no. 5, 1209 …
Burns, Climenhaga, Fisher, and Thompson [Geom. Funct. Anal. 28 (2018), no. 5, 1209 …
Finite measures of maximal entropy for an open set of partially hyperbolic diffeomorphisms
J Mongez, M Pacifico - Transactions of the American Mathematical Society, 2024 - ams.org
We consider partially hyperbolic diffeomorphisms $ f $ with a one-dimensional central
direction such that the unstable entropy is different from the stable entropy. Our main result …
direction such that the unstable entropy is different from the stable entropy. Our main result …
Beyond Bowen's specification property
A classical result in thermodynamic formalism is that for uniformly hyperbolic systems, every
Hölder continuous potential has a unique equilibrium state. One proof of this fact is due to …
Hölder continuous potential has a unique equilibrium state. One proof of this fact is due to …
Robustness and uniqueness of equilibrium states for certain partially hyperbolic systems
JC Mongez, MJ Pacifico - arxiv preprint arxiv:2306.12323, 2023 - arxiv.org
arxiv:2306.12323v1 [math.DS] 21 Jun 2023 Page 1 arxiv:2306.12323v1 [math.DS] 21 Jun 2023
ROBUSTNESS AND UNIQUENESS OF EQUILIBRIUM STATES FOR CERTAIN PARTIALLY …
ROBUSTNESS AND UNIQUENESS OF EQUILIBRIUM STATES FOR CERTAIN PARTIALLY …
Specification and towers in shift spaces
V Climenhaga - Communications in Mathematical Physics, 2018 - Springer
We show that a shift space on a finite alphabet with a non-uniform specification property can
be modeled by a strongly positive recurrent countable-state Markov shift to which every …
be modeled by a strongly positive recurrent countable-state Markov shift to which every …
[HTML][HTML] Zero-entropy dynamical systems with the gluing orbit property
P Sun - Advances in Mathematics, 2020 - Elsevier
Under the assumption of the gluing orbit property, equivalent conditions to having zero
topological entropy are investigated. In particular, we show that a dynamical system has the …
topological entropy are investigated. In particular, we show that a dynamical system has the …
Equilibrium states for partially hyperbolic diffeomorphisms with hyperbolic linear part
We address the problem of existence and uniqueness (finiteness) of ergodic equilibrium
states for a natural class of partially hyperbolic dynamics homotopic to Anosov. We propose …
states for a natural class of partially hyperbolic dynamics homotopic to Anosov. We propose …