Nineteenth century anticipations of modern theory of dynamical systems

Abstract

The “Laplace demon”, an intelligence capable of knowing the position and the velocity of every particle in the universe and so, using the laws of classical physics, knowing all their future states, seemed in the last century to pose a contradiction between the laws of physics and the freedom of the human will. In addressing this apparent paradox, Maxwell, Boussinesq and Saint-Venant were led to consider aspects of the theory of systems of differential equations. These aspects, though for different reasons, have come to assume a central place in the modern theory of dynamical systems.