# Talk:Chaotic hypothesis

This is an excellent article and I fully endorse publication. However the phrasing of the hypothesis might be difficult to understand for some readers. Here are some observations.

The notion "chaotic system" remains undefined. If it is a physical notion, how would one distinguish between chaotic and non chaotic. If it is a mathematical notion, the author seems to suggest that he requires a positive maximal Lyapunov exponent.

"can be regarded" presumably wants to say with respect to the small set of observables of interest. Does "asymptotically" refer to the time scale of interest or to the truly stationary regime?

Physically chaotic means that data initially close separate exponentially fast in time mathematically this means that there is at least one positive Lyapunov exponents. Non chaotic is the negation of chaotic: I have stated tis explicitly

For the second remark I have stressed the analogy with the ergodic hypothesis: it concerns both the approach to stationarity (ie the aproach to the attractor) and the motion on the attractor itself. As in the case of the ergodic hypothesis it deals only with a few properties of relevance for the macroscopic behavior of the system. Which ones precisely? that is discussed in the following of the paper ("interest of CH"...: they have to be analyzed on a case by case basis, recisely as in the case of the ergodic hypothesis. I have added comments in this sense. It is also interesting to stress that the very first example of a mechanical system which is ergodic in a mathematical sense was in fact that of a chaotic system in the mathematical sense.