Dong Chen - PSU Mathematics PhD Student

Dong Chen

Personal Information

I am a Ph.D. graduate in Department of Mathematics. My advisor is Dmitri Burago. My research is focused on differential geometry and dynamical systems. It includes problems from KAM theory, inverse problems, hyperbolicity, Finsler geometry, Aubry-Mather theory etc. I am particularly interested in the interaction between KAM-nondegenrate nearly integrable systems and geodesic flows. I will move to the Ohio State University as a Zassenhaus Assistant Professor from August 2017.

CV/Resume

Research Interests

  • Riemannian Geometry, Finsler Geometry, Lagrangian Mechanics
  • KAM Theory, Geodesic Flows, Ergodic Theory

    Publications

  • Positive metric entropy arises in some nondegenerate nearly integrable systems.
    Journal of Modern Dynamics, vol. 11, pp. 43-56, 2017.
  • On total flexibility of local structures of Finsler tori without conjugate points.
    Submitted.
  • An example of entropy non-expansive nearly integrable system. Manuscript in preparation. (Joint with D. Burago and S. Ivanov).
  • Nondense geodesics with irrational rotational vector in C^\infty-small perturbation of flat tori. Manuscript in preparation(Joint with D. Burago).

  • Teaching

  • MATH 021 - College Algebra I (FA12, SP13, FA15, SP16)
  • MATH 230 - Calculus and Vector Analysis (FA14, SP15, SP17)
  • Seminars and Interesting Things


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