20 citations · 34 across the 11 of their papers we have counts for
11 papers
A remark on the phase transition for the geodesic flow of a rank one surface of nonpositive curvature
Keith Burns, Dong Chen
For any rank 1 nonpositively curved surface , it was proved by Burns-Climenhaga-Fisher-Thompson that for any , there exists a unique equilibrium state for , whe…
Pressure gaps, geometric potentials, and nonpositively curved manifolds
Dong Chen, Lien-Yung Kao, Kiho Park
In this paper, we derive a general pressure gap criterion for closed rank 1 manifolds whose singular sets are given by codimension 1 totally geodesic flat subtori. As an applicatio…
Riemannian Anosov extension and applications
Dong Chen, Alena Erchenko, Andrey Gogolev
Let be a Riemannian manifold with strictly convex spherical boundary. Assuming absence of conjugate points and that the trapped set is hyperbolic, we show that can be isome…
Flexibility of sections of nearly integrable Hamiltonian systems
Dmitri Burago, Dong Chen, Sergei Ivanov
Given any symplectomorphism on which is close to the identity, and any completely integrable Hamiltonian system in the proper dimension, we…
Key ideas behind perturbing any completely integrable Hamiltonian system obtaining volume entropy non-expansiveness
Dmitri Burago, Dong Chen, Sergei Ivanov
This paper is an announcement of a result followed with explanations of some ideas behind. The proofs will appear elsewhere. Our goal is to construct a Hamiltonian perturbation of…
Properties of equilibrium states for geodesic flows over manifolds without focal points
Dong Chen, Lien-Yung Kao, Kiho Park
We prove that for closed rank 1 manifolds without focal points the equilibrium states are unique for Hölder potentials satisfying the pressure gap condition. In addition, we provid…