79 citations · 484 across the 27 of their papers we have counts for
33 papers
Effective uniqueness of the measure of maximal entropy in Ornstein's -metric
Vaughn Climenhaga, Teena Kumari
Every topologically mixing shift of finite type has a unique measure of maximal entropy. It follows from Ornstein theory that every invariant measure with entropy close to maximal…
Thermodynamic formalism for non-compact systems with expansivity and specification
Vaughn Climenhaga, Daniel J. Thompson, Tianyu Wang
We develop the theory of equilibrium states via specification properties for a wide class of continuous flows on complete separable metric spaces. We provide general dynamical crit…
Every finite horizon Sinai billiard map has a unique measure of maximal entropy
Vaughn Climenhaga, Jason Day
Finite horizon Sinai billiard maps are examples of uniformly hyperbolic systems with singularities. These discontinuities make it more difficult to develop the classical theory of…
A Nonstationary Ruelle-Perron-Frobenius Theorem
Vaughn Climenhaga, Gregory Hemenway
The Ruelle-Perron-Frobenius theorem is a powerful tool in the study of equilibrium measures and their statistical properties. We prove a nonstationary version of this theorem under…
Maximizing entropy for power-free languages
Vaughn Climenhaga
A power-free language is characterized by the number of symbols used and a limit on how many times a block of symbols can repeat consecutively. For certain values of these paramete…
Gibbs measures have local product structure
Vaughn Climenhaga
It is well-known that equilibrium measures for uniformly hyperbolic dynamical systems have a local product structure, which plays an important role in their mixing properties. Exis…
Equilibrium measures for two-sided shift spaces via dimension theory
Vaughn Climenhaga, Jason Day
Given a two-sided shift space on a finite alphabet and a continuous potential function, we give conditions under which an equilibrium measure can be described using a construction…
Lyapunov exponents and nonadapted measures for dispersing billiards
Vaughn Climenhaga, Mark Demers, Yuri Lima +1
For hyperbolic systems with singularities, such as dispersing billiards, Pesin theory as developed by Katok and Strelcyn applies to measures that are "adapted" in the sense that th…
SRB and equilibrium measures via dimension theory
Vaughn Climenhaga
It is well-known that SRB and equilibrium measures for uniformly hyperbolic flows admit a product structure in terms of measures on stable and unstable leaves with scaling properti…
Beyond Bowen's Specification Property
Vaughn Climenhaga, Daniel J. Thompson
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…
Closed geodesics on surfaces without conjugate points
Vaughn Climenhaga, Gerhard Knieper, Khadim War
We obtain Margulis-type asymptotic estimates for the number of free homotopy classes of closed geodesics on certain manifolds without conjugate points. Our results cover all compac…
SRB measures and Young towers for surface diffeomorphisms
Vaughn Climenhaga, Stefano Luzzatto, Yakov Pesin
We give geometric conditions that are necessary and sufficient for the existence of Sinai-Ruelle-Bowen (SRB) measures for surface diffeomorphisms, thus proving a version…
Uniqueness of the measure of maximal entropy for geodesic flows on certain manifolds without conjugate points
Vaughn Climenhaga, Gerhard Knieper, Khadim War
We prove that for closed surfaces with Riemannian metrics without conjugate points and genus the geodesic flow on the unit tangent bundle has a unique measure o…
Equilibrium measures for some partially hyperbolic systems
Vaughn Climenhaga, Yakov Pesin, Agnieszka Zelerowicz
We study thermodynamic formalism for topologically transitive partially hyperbolic systems in which the center-stable bundle satisfies a bounded expansion property, and show that e…
Equilibrium states in dynamical systems via geometric measure theory
Vaughn Climenhaga, Yakov Pesin, Agnieszka Zelerowicz
Given a dynamical system with a uniformly hyperbolic (`chaotic') attractor, the physically relevant Sinai-Ruelle-Bowen (SRB) measure can be obtained as the limit of the dynamical e…
Positive entropy equilibrium states
Vaughn Climenhaga, Van Cyr
For transitive shifts of finite type, and more generally for shifts with specification, it is well-known that every equilibrium state for a Holder continuous potential has positive…
Unique equilibrium states for geodesic flows in nonpositive curvature
Keith Burns, Vaughn Climenhaga, Todd Fisher +1
We study geodesic flows over compact rank 1 manifolds and prove that sufficiently regular potential functions have unique equilibrium states if the singular set does not carry full…
The geometric approach for constructing Sinai-Ruelle-Bowen measures
Vaughn Climenhaga, Stefano Luzzatto, Yakov Pesin
An important class of `physically relevant' measures for dynamical systems with hyperbolic behavior is given by Sinai-Ruelle-Bowen (SRB) measures. We survey various techniques for…
One-sided almost specification and intrinsic ergodicity
Vaughn Climenhaga, Ronnie Pavlov
Shift spaces with the specification property are intrinsically ergodic, i.e. they have a unique measure of maximal entropy. This can fail for shifts with the weaker almost specific…
Unique equilibrium states for Bonatti-Viana diffeomorphisms
V. Climenhaga, T. Fisher, D. J. Thompson
We show that the robustly transitive diffeomorphisms constructed by Bonatti and Viana have unique equilibrium states for natural classes of potentials. In particular, we characteri…
Unique equilibrium states for flows and homeomorphisms with non-uniform structure
Vaughn Climenhaga, Daniel J. Thompson
Using an approach due to Bowen, Franco showed that continuous expansive flows with specification have unique equilibrium states for potentials with the Bowen property. We show that…
Specification and towers in shift spaces
Vaughn Climenhaga
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 ever…
Non-stationary non-uniform hyperbolicity: SRB measures for dissipative maps
Vaughn Climenhaga, Dmitry Dolgopyat, Yakov Pesin
We prove the existence of SRB measures for diffeomorphisms where a positive volume set of initial conditions satisfy an "effective hyperbolicity" condition that guarantees certain…
Large deviations for systems with non-uniform structure
Vaughn Climenhaga, Daniel J. Thompson, Kenichiro Yamamoto
We use a weak Gibbs property and a weak form of specification to derive level-2 large deviations principles for symbolic systems equipped with a large class of reference measures.…