Abstract:
Poincaré's Recurrence Theorem (which appears as Theorem I in his
celebrated Acta Mathematica paper "Sur le problème des trois corps
et les equations de la dynamique") was originally intended to
facilitate the study of stability of the solar system. After briefly
discussing the history and some applications of Poincaré's
Recurrence Theorem in the kinetic theory of gases, we will focus on
some modern enhancements and generalizations of it which lead to
strong applications in combinatorics and number theory. We will
conclude with discussion of some natural open problems and
conjectures. The talk is intended for a general audience.
