A link between Topological Entropy and Lyapunov Exponents
arXiv:1601.04025 · doi:10.1017/etds.2017.39
Abstract
We show that a generic non partially hyperbolic symplectic diffeomorphism 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 has topological entropy approximated by the topological entropy of restrict to basic hyperbolic sets. In particular, the topological entropy map is lower semicontinuous in a generic set of symplectic diffeomorphisms far from partial hyperbolicity.
17 pages