Computer assisted studies in dynamical systems

It is a well known fact that purely analytical methods are suitable to prove existence results and to get some local or semiglobal information on the dynamics of a system. If a more detailed study is desired or, in many cases, if one has to guess first the properties to be proven, we have to proceed to do a computer assisted study of the problem. In these notes I summarize several domains where a systematic use of a computer can help us to learn about a given family of dynamical systems and provide some examples.