1: Introduction

In his 1954 plenary address to the International Congress of Mathematicians in Amsterdam, the Russian mathematician Andrey Kolmogorov announced a theorem that wowed the mathematical world. Mathematicians quickly realized that, if true as stated, the theorem resolved a paradox that had stood since Henri Poincaré's work at the end of the 19th century, and possibly also invalidated Ludwig Boltzmann's ergodic hypothesis that lay at the foundations of statistical mechanics. Even more, if the theorem could be successfully applied to models of planetary motion based on Newtonian physics, the centuries-old goal of showing that the solar system is stable might finally be reached…