EVENT DETAILS AND ABSTRACT

Title: On Herman's oldest open question in dynamics and diffusion along mean motion resonance for the restricted planar three body problem (joint with J. Fejoz, M. Giardia, P. Roldan)
Speaker: Vadim Kaloshin
Speaker Info: University of Maryland
Brief Description:
Special Note:
Abstract:

Herman's oldest open question in dynamics, in particular, claims that for an open dense set of initial conditions of a 3 body problem orbits are unbounded. We make a small step toward this conjecture. We consider a planar 3 body problem so that one body is large (the Sun), one small (Jupiter), and the other is tiny (Asteroid). In the regime when period of Jupiter and of Asteroid are in resonance (called mean motion resonance) 1:7 we show that orbit of Asteroid can substantially change its shape. This 1:7 resonance is close to mean motion resonance between Jupiter and Uranus. The proof is computer assisted with fundamental role played by apriori unstable structure of the underlying Hamiltonian system.