If we have a Markov coding or another symbolic description of a dynamical system it is usually easy to prove that the system is chaotic (in the sense of of Li-York, Devaney, positive entropy of what ever). My impression is that most (interesting) dynamical systems coming of natural science are in fact chaotic. But this is rigourously proved only for a few systems. What is the reason for this? Is it difficult to find a symbolic coding for systems coming from natural science or are we (as mathematicians) not so much interested in these systems?