Publicação: C1-Genericity of symplectic diffeomorphisms and lower bounds for topological entropy
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There is a C1-residual (Baire second class) subset R of symplectic diffeomorphisms on 2d-dimensional manifold, d ≥ 1, such that for every non-Anosov f in R, its topological entropy is lower bounded by the supremum of the Lyapunov exponents of their hyperbolic periodic points in the unbreakable central sub-bundle (i.e. central direction with no dominated splitting) of f. The previous result deals with the fact that for f in a C1-residual set R of symplectic diffeomorphisms (containing R) satisfies a trichotomy: or f is Anosov or f is robustly transitive partially hyperbolic with unbreakable centre of dimension 2m, 0 < m < d, or f has totally elliptic periodic points dense on M. In the second case, we also show the existence of a sequence of m-elliptic periodic points converging to M. Indeed, R contains an C1 open and dense subset of symplectic diffeomorphisms.
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elliptic periodic points, generic properties, homoclinic tangency, Partially hyperbolic symplectic systems, topological entropy
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Inglês
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Dynamical Systems, v. 32, n. 4, p. 461-489, 2017.
