A link between Topological Entropy and Lyapunov Exponents
Abstract
We show that a C1-generic non partially hyperbolic symplectic diffeomorphism f has topological entropy equal to the supremum of the sum of the positive Lyapunov exponents of its hyperbolic periodic points. Moreover, we also prove that f has topological entropy approximated by the topological entropy of f restrict to basic hyperbolic sets. In particular, the topological entropy map is lower semicontinuous in a C1-generic set of symplectic diffeomorphisms far from partial hyperbolicity.
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