[Queen's University] [Department of Mathematics and Statistics]

Daniel C. Offin

Associate Professor


Department of Mathematics and Statistics,
Queens University, Kingston Canada
Kingston, Ontario, Canada, K7L 3N6


My research interests

include dynamical systems, celestial mechanics, symplectic geometry, and global variational methods. I have a special interest in variational methods which may be used to determine stability and instability of periodic and almost periodic solutions in Hamiltonian systems. The three body problem of celestial mechanics combining all the topics mentioned above, is currently an active and exciting subject with many open problems. Current interest is focused on understanding how the braid structure of the figure eight solution, may be used to give an analytic explanation of the stability properties.

My recent publication

Hyperbolic mimimizing geodesics, Trans. Amer. Math. Soc., 352(2000) No 7, answers a conjecture of G.D. Birkhoff on instability of closed minimizing geodesics on N-dimensional Riemannian manifolds. The technique presented in this paper is currently being used to study instability of the figure eight orbit, in the full three body problem, discovered recently by Chenciner and Montgomery. The main theoretical tool used to establish an important connection between stability theory and variational theory, is a new comparison theory for intersection numbers of Lagrangian submanifolds in a symplectic manifold. You can download a postscript file copy of this paper now by clicking hyperbolic.

A second paper on a similar theme

Variational structure on the zones of instability, Differential and Integral Equations (1991), stability explores this connection in greater detail in the more elementary setting of scalar second order equations (one dimensional , time periodic Schroedinger equations). Here the phenomenon of parametric resonance is explored using a variational approach, rather than the traditional method based on Liapunov multipliers. The main theoretical tool used is the Maslov index for closed curves of Lagrangian submanifolds, which in this setting is shown to be the same as the winding number of a nontrivial solution in the complex plane.

You can send me an email message by clicking on the address below.

Email: offind@mast.queensu.ca

According to the penguin... I really dont know how this fellow got on my web page!