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Dong Chen, Ph.D.

Assistant Research Professor
Department of Mathematics, Eberly College of Science
Pennsylvania State University
231 McAllister Building, University Park, PA 16802
dxc360@psu.edu

 

Research Interests

My research interests are focused on geometry, dynamical systems, and inverse problems. My research is currently supported by the AMS-Simons Travel Grant. Here is my CV.

 

Publications and preprints

  • “Riemannian Anosov extension and applications” (joint with A. Erchenko and A. Gogolev), manuscript available at arxiv.org/abs/2009.13665. Under review.
  • “On the closing lemma for Hamiltonian flows on symplectic 4-manifolds”, manuscript available at arxiv.org/abs/1904.09900. Under review.
  • “An example of entropy non-expansive nearly integrable system” (joint with Dmitri Burago and Sergei Ivanov), accepted by Communications in Contemporary Mathematics.
  • “Finsler perturbation with non-dense geodesics with irrational directions” (joint with Dmitri Burago), accepted by Asian Journal of Mathematics.
  • “Properties of equilibrium states for geodesic flows without focal points” (joint with Lien-Yung Kao and Kiho Park), Advances in Mathematics, 380 (2021), 107564.
  • “Unique equilibrium states for geodesic flows over surfaces without focal points” (joint with Lien-Yung Kao and Kiho Park), Nonlinearity, 33 (2020), no. 3, 1118-1155.
  • “On total flexibility of local structures of Finsler tori without conjugate points”, Journal of Topology and Analysis, Vol. 11 (2019), No. 02, pp. 349-355.
  • “Positive metric entropy arises in some nondegenerate nearly integrable systems”, Journal of Modern Dynamics, Vol. 11 (2017), pp. 43-56.

Research note

  • “The key ideas behind perturbing any completely integrable Hamiltonian system obtaining metric entropy non-expansiveness” (joint with Dmitri Burago and Sergei Ivanov), manuscript available at arxiv.org/abs/2009.10143.

Teaching Experience

Course Instructor, Department of Mathematics, The Pennsylvania State University

Course Instructor, Department of Mathematics, The Ohio State University