Is there positive metric entropy (“chaos”) in a given conservative dynamical system?
” One of many definitions of “chaos” in a Hamiltonian system is the property of having positive metric entropy. Hamiltonian systems with this property show sensitive dependence on initial conditions on a set of positive measure. Moreover, one can find quantities accessible to measurements which are actually independent random variables. The system could be used as a true random number generator ! (We refer to the Les Houches Lecture of Lanford [Lan 83], the Bernard Lecture [Rue 90] or the Lezioni Lincee [Rue 87] of Ruelle for an introduction into some of the topics.) From the physical point of view, there is evidence that chaos is the rule and zero metric entropy is the exception. The entropy has been measured in many systems and found to be positive. It seems, however, that mathematical proofs for chaos are difficult. It could even be that most measurements show numerical artifacts and that positive metric entropy is the exception. There are milder requirements for a system to belong
