Dynamical Systems. Catastrophes and Chaos

Abstract

In 1776, ninety years after the apparition of the fundamental treatise of Newton, Laplace enounces his famous principle of the determinism, stating that: “The actual stage of the system of nature is, obviously, a consequence of that it was at the preceding moment and, if we imagine an intelligence, which – at a given moment – knows all the relations between entities of this universe, then it could establish the respective positions and the motions of all these entities, at any moment in the past or in the future” This determinism is – in fact – a mechanistic determinism. But Laplace continues: … “there exist things which are uncertain for us, things which are more or less probable and we try to counter-balance the impossibility to know them, determining various degrees of probability”.