Dong Chen

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20182022

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math.DS2022

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 $M$ , it was proved by Burns-Climenhaga-Fisher-Thompson that for any $q < 1$ , there exists a unique equilibrium state $μ_{q}$ for $q φ^{u}$ , whe…

math.DS2019

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…

math.DS2019

On the $C^{\infty}$ closing lemma for Hamiltonian flows on symplectic $4$ -manifolds

Dong Chen

The main result in this paper is the $C^{\infty}$ closing lemma for a large family of Hamiltonian flows on $4$ -dimensional symplectic manifolds, which includes classical Hamiltonia…

math.DS2018

Unique equilibrium states for geodesic flows over surfaces without focal points

Dong Chen, Lien-Yung Kao, Kiho Park

In this paper, we study dynamics of geodesic flows over closed surfaces of genus greater than or equal to 2 without focal points. Especially, we prove that there is a large class o…

A remark on the phase transition for the geodesic flow of a rank one surface of nonpositive curvature

Properties of equilibrium states for geodesic flows over manifolds without focal points

On the C∞ closing lemma for Hamiltonian flows on symplectic 4-manifolds

Unique equilibrium states for geodesic flows over surfaces without focal points

On the $C^{\infty}$ closing lemma for Hamiltonian flows on symplectic $4$ -manifolds