Computability and dynamical systems

In this paper we explore results that establish a link between dynamical systems and computability theory (not numerical analysis). In the last few decades, computers have increasingly been used as simulation tools for gaining insight into dynamical behavior. However, due to the presence of errors inherent in such numerical simulations, with few exceptions, computers have not been used for the nobler task of proving mathematical results. Nevertheless, there have been some recent developments in the latter direction. Here we introduce some of the ideas and techniques used so far, and suggest some lines of research for further work on this fascinating topic