79 citations · 328 across the 18 of their papers we have counts for
20 papers
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…
Fluctuations of time averages around closed geodesics in non-positive curvature
Daniel J. Thompson, Tianyu Wang
We consider the geodesic flow for a rank one non-positive curvature closed manifold. We prove an asymptotic version of the Central Limit Theorem for families of measures constructe…
Learning medical triage from clinicians using Deep Q-Learning
Albert Buchard, Baptiste Bouvier, Giulia Prando +10
Medical Triage is of paramount importance to healthcare systems, allowing for the correct orientation of patients and allocation of the necessary resources to treat them adequately…
Measures of maximal entropy on subsystems of topological suspension semi-flows
Tamara Kucherenko, Daniel J. Thompson
Given a compact topological dynamical system (X, f) with positive entropy and upper semi-continuous entropy map, and any closed invariant subset with positive entropy…
Equilibrium states for self-products of flows and the mixing properties of rank 1 geodesic flows
Benjamin Call, Daniel J. Thompson
Equilibrium states for geodesic flows over closed rank 1 manifolds were studied recently by Burns, Climenhaga, Fisher and Thompson. For sufficiently regular potentials, it was show…
Strong symbolic dynamics for geodesic flow on CAT(-1) spaces and other metric Anosov flows
David Constantine, Jean-François Lafont, Daniel J. Thompson
We prove that the geodesic flow on a locally CAT(-1) metric space which is compact, or more generally convex cocompact with non-elementary fundamental group, can be coded by a susp…
Measures of maximal entropy for suspension flows over the full shift
Tamara Kucherenko, Daniel J. Thompson
We consider suspension flows with continuous roof function over the full shift on a finite alphabet. For any positive entropy subshift of finite type , we explictl…
Fat flats in rank one manifolds
D. Constantine, J. -F. Lafont, D. B. McReynolds +1
We study closed non-positively curved Riemannian manifolds which admit `fat -flats': that is, the universal cover contains a positive radius neighborhood of a …
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…
Equilibrium states for Mañé diffeomorphisms
V. Climenhaga, T. Fisher, D. J. Thompson
We study thermodynamic formalism for the family of robustly transitive diffeomorphisms introduced by Mañé, establishing existence and uniqueness of equilibrium states for natural c…
The weak specification property for geodesic flows on CAT(-1) spaces
David Constantine, Jean-François Lafont, Daniel J. Thompson
We prove that the geodesic flow on a compact locally CAT(-1) space has the weak specification property, and give various applications. We show that every Hölder potential on the sp…
Generalized beta-transformations and the entropy of unimodal maps
Daniel J. Thompson
Generalized beta-transformations are the class of piecewise continuous interval maps given by taking the beta-transformation , where , and replacing som…
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…
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.…
Intrinsic ergodicity via obstruction entropies
Vaughn Climenhaga, Daniel J. Thompson
Bowen showed that a continuous expansive map with specification has a unique measure of maximal entropy. We show that the conclusion remains true under weaker non-uniform versions…
Coding Sequence Density Estimation Via Topological Pressure
David Koslicki, Daniel J. Thompson
We give a new approach to coding sequence (CDS) density estimation in genomic analysis based on the topological pressure, which we develop from a well known concept in ergodic theo…
Equilibrium states beyond specification and the Bowen property
Vaughn Climenhaga, Daniel J. Thompson
It is well-known that for expansive maps and continuous potential functions, the specification property (for the map) and the Bowen property (for the potential) together imply the…
Intrinsic ergodicity beyond specification: beta-shifts, S-gap shifts, and their factors
Vaughn Climenhaga, Daniel J. Thompson
We give sufficient conditions for a shift space to be intrinsically ergodic, along with sufficient conditions for every subshift factor of to be intrinsically ergodic.…
A criterion for topological entropy to decrease under normalised Ricci flow
Daniel J. Thompson
In 2004, Manning showed that the topological entropy of the geodesic flow for a surface of negative curvature decreases as the metric evolves under the normalised Ricci flow. It is…
Irregular sets, the -transformation and the almost specification property
Daniel J. Thompson
Let be a compact metric space, be a continuous map satisfying a property we call almost specification (which is slightly weaker than the -almost product…