Conférence Nirenberg en analyse géométrique
Conférence de Vadim Kaloshin, titulaire de la chaire Michael Brin en mathématiques de l'Université du Maryland. Il a obtenu son doctorat de l'Université de Princeton en 2001 sous la supervision de John Mather. Le professeur Kaloshin a apporté des contributions fondamentales à la théorie des systèmes dynamiques, notamment à l'étude de la diffusion d'Arnold, du problème à n corps et de la conjecture de Birkhoff pour le billard convexe.
Résumé:
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.
