Computability and computational complexity of the evolution of nonlinear dynamical systems

Abstract

Nonlinear dynamical systems abound as models of natural phenomena. They are often characterized by highly unpredictable behaviour which is hard to analyze as it occurs, for example, in chaotic systems. A basic problem is to understand what kind of information we can realistically expect to extract from those systems, especially information concerning their long-term evolution. Here we review a few recent results which look at this problem from a computational perspective. © 2013 Springer-Verlag.