摘要
Lyapunov exponents and entropy have been discussed repeatedly during the International Summer School on Chaos (Beijing, 1987). Physicists seemed to regard them as the same thing. Whenever they find positive Lyapunov exponents in experiments, they claim they find chaos. But so far as we know, the relationship between positive Lyapunov exponents and positive metric entropy is not dear mathematically. Suppose M is smooth Riemannian dosed manifold, f∈Diff^2(M), m is a Borel ergodic measure off, W^1(?)
