Vadim Kaloshin, University of Maryland
Title: Conf茅rence Nirenberg du CRM en analyse g茅om茅trique: Stochastic diffusive behavior at Kirkwood gaps
Abstract: One of the well known indications of instability in the Solar system is the presence of Kirkwood gaps in the Asteroid belt. The gaps correspond to resonance between their periods and the period of Jupiter. The most famous ones are period ratios 3:1, 5:2, 7:3. In the 1980s, J. Wisdom and, independently, A. Neishtadt discovered one mechanism of creation for the 3:1 Kirkwood gap. We propose another mechanism of instabilities, based on an a priori chaotic underlying dynamical structure. As an indication of chaos at the Kirkwood gaps, we show that the eccentricity of Asteroids behaves like a stochastic diffusion process. Along with the famous KAM theory this shows a mixed behavior at the Kirkwood gaps: regular and stochastic. This is a joint work with M. Guardia, P. Martin and P. Roldan.
(Cette conf茅rence s'adresse 脿 un large auditoire. / This lecture is aimed at a general mathematical audience.)