  We show that existence of positive Lyapounov exponents and/or SRB measures
are undecidable (in the algorithmic sense) properties within some parametrized
families of interesting dynamical systems: quadratic family and H\'enon maps.
Because the existence of positive exponents (or SRB measures) is, in a natural
way, a manifestation of ``chaos'', these results may be understood as saying
that the chaotic character of a dynamical system is undecidable. Our
investigation is directly motivated by questions asked by Carleson and Smale in
this direction.
