### Is there a Natural Dynamics for Systems with Many Degrees of Freedom?

**David Ruelle**

Institut des Hautes Etudes Scientifiques, France

KAM theory and the Fermi-Pasta-Ulam experiments show that large systems can

have nonhyperbolic behavior. Statistical mechanics seems however to

conform to an interpretation based on uniform hyperbolicity and SRB states

(at equilibrium and also outside of equilibrium). How can one reconcile

this interpretation with the fact that real systems are probably not

uniformly hyperbolic? We shall discuss some facts (about SRB states and

their dependence on parameters) and some possibilities.

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