  The physical Church thesis is a thesis about nature that expresses that all
that can be computed by a physical system-a machine-is computable in the sense
of computability theory. At a first look, this thesis seems contradictory with
the existence, in nature, of chaotic dynamical systems, that is systems whose
evolution cannot be ''computed'' because of their sensitivity to initial
conditions. The goal of this note is to show that there exist dynamical systems
that are both computable and chaotic, and thus that the existence in nature of
chaotic dynamical system is not, per se, a refutation of the physical Church
thesis. Thus, chaos seems to be compatible with computability, in the same way
as it is compatible with determinism.
