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Eunice Kim
Norbert Wiener Assistant Professor
Patricia Garmirian
Contact Info:
Tufts University
Department of Mathematics
503 Boston Avenue
Medford, MA 02155

Email @tufts.edu:
Phone: 617-627-6308

Dynamical systems

My primary research area is dynamical systems, especially billiards, chaos theory, classical mechanics, differential equations, and the applications of these theories to the study of physical phenomena. For example, my recent work involves investigating the stability of a system of coupled pendulums using Floquet theory, a study of periodic linear ordinary differential equations. I've also been exploring mathematical billiards and its connection to Hamiltonian systems with impacts.

Billiards is the study of the free motion of a point in a bounded region. Billiards appeared in the 1960's in the context of Boltzmann ergodic hypothesis to study ideal gas, and since then it has served as a useful model for physical systems with impacts. More recently, non-spherical particles, which have rotational in addition to translational velocities, were studied to build a more realistic gas model. In this direction, my recent interests have been on the behavior of a two-dimensional object moving inside a simple domain, sometimes with an external force. It turns out that the extra degree of freedom of a moving object can generate many interesting phenomena including deterministic chaos and adiabatic invariance.

Abstract theories in billiards turned out to be useful beyond the original physical application. The systematic study of billiards in the Euclidean plane has been extended to different settings, such as non-Euclidean spaces and higher dimensional spaces. My research in particular focuses on periodic orbits in billiards on the hyperbolic plane and on the sphere.