Norbert Wiener Assistant Professor
Department of Mathematics
503 Boston Avenue
Medford, MA 02155
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.