Wada Basins and Unpredictability in Hamiltonian and Dissipative Systems

Abstract

Prediction is one of the fundamental goals of science. When prediction is lost, it can be thought that one of the foundations of science is shattered. The notion of a chaotic system and the sensitive dependence on initial conditions implies a certain lack of prediction on the time evolution along an orbit. However we do not speak here about this temporal prediction, but about an extreme dependence on the initial conditions that fractal structures in phase space impose, and that obstructs the prediction of the final state of the system.