Determinism versus predictability in the context of Poincare's work on the restricted 3-body problem

Abstract

It is exposed the Poincare’s work (1880's) in the system defining the restricted 3-body problem which led to the discovery of a special kind of behavior – the dynamical instability. Contrary to the widespread belief that the Deterministic Chaos Theory began with the computational work of Lorenz (1960's), the Poincare's theoretical research was sufficiently clear about the existence of chaotic deterministic behavior. Until the time of Poincare, there was a tacit assumption that the uncertainty in the output does not arise from any randomness in the dynamical laws, since they are completely deterministic, but rather from the lack of the infinite accuracy in the initial conditions. In this paper it is emphasized that the issues of determinism and predictability are distinct.