12/7/2005

V. Kaloshin
Caltech/Penn State

Nonlocal instability of the planar 3 body problem

The Restricted Planar Circular 3 Body Problem (RPC3BP) which is the simplest nonintegrable 3 body problem. Usually it is viewed as a model for planar either Sun-Jupiter-Asteriod or Sun-Earth-Moon system. Stability v.s. instability of such a system is one of long standing problems. Using Aubry-Mather
theory, Mather variational method, and numerical analysis, we managed to prove existence of rich variety of unstable motions. For example, an Asteriod could have a nearly elliptic orbit of say eccenticity 0.76 in the past and escape to infinity along nearly parabolic orbit of eccentricity more than 1 in the future. These motions could be interpreted as Arnold diffusion for this system. Instability results for RPC3BP imply instability for more general planar 3 body problems. This is a joint work with T. Nguyen and D. Pavlov.