Vadim Kaloshin, Univ. of Maryland and ETH Zürich
Title: Stochastic Arnold Diffusion of Deterministic Systems
Abstract: In 1964, V. Arnold constructed an example of a nearly integrable deterministic system
exhibiting instabilities. In the 1970s, physicist B. Chirikov coined the term for this phenomenon
"Arnold diffusion", where diffusion refers to stochastic nature of instability. One of the most famous
examples of stochastic instabilities for nearly integrable systems is dynamics of Asteroids in
Kirkwood gaps in the Asteroid belt. They were discovered numerically by astronomer J. Wisdom.
During the talk we describe a class of nearly integrable deterministic systems, where we prove
stochastic diffusive behavior. Namely, we show that distributions given by deterministic evolution
of certain random initial conditions weakly converge to a diffusion process. This result is conceptually
different from known mathematical results, where existence of "diffusing orbits" is shown. This work
is based on joint papers with O. Castejon, M. Guardia, J. Zhang, and K. Zhang.