Non - Zero Lyapunov Exponents and Axiom
نویسنده
چکیده
Let f : M → M be a C 1 diffeomorphism of a compact manifold M admitting a dominated splitting T M = E cs ⊕ E cu. We show that if the Lyapunov exponents of f are nonzero and have the same sign along the E cs and E cu directions on a total probability set (a set with probability one with respect to every f-invariant measure), then f is Axiom A. We also show that a f-ergodic measure whose Lyapunov exponents are all negative must be concentrated on the orbit of a sink (without using Hölder continuity on the derivative Df).
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