Computability and information in models of randomness and chaos

This paper presents a short survey of some recent approaches relating different areas: deterministic chaos and computability. Chaos, in classical physics, may be approached by dynamical (equationally determined) systems or stochastic ones (as random processes). Now, randomness has also been effectively modeled with recursion theoretic tools by P. Martin-Löf. We recall its connections to Kolmogorov complexity and show some applications to dynamical systems. This allows to introduce connecting results between well established notions of entropy and algorithmic information.