activity
20092020
most citedIntrinsic ergodicity beyond specification: beta-shifts, S-gap shifts, and their factors

79 citations · 328 across the 18 of their papers we have counts for

collaborators

20 papers

math.DS2020

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…

math.DS2020★ 2 cited

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…

cs.AI2020★ 2 cited

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…

math.DS2019

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…

math.DS2019★ 22 cited

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…

math.DS2018★ 12 cited

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…

math.DS2017

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…

math.DS2017★ 3 cited

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 …

math.DS2017★ 1 cited

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…

math.DS2017★ 3 cited

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…

math.DS2016★ 4 cited

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…

math.DS2016

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…

math.DS2015★ 79 cited

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…

math.DS2013★ 39 cited

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.…

math.DS2012★ 17 cited

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…

math.DS2011

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…

math.DS2011★ 64 cited

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…

math.DS2010★ 79 cited

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.…

math.DS2009★ 1 cited

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…

math.DS2009

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…