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C~1-Genericity of symplectic diffeomorphisms and lower bounds for topological entropy

机译：辛熵的C〜1-一般性和拓扑熵的下界

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摘要

There is a C~1-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 C~1-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 C~1 open and dense subset of symplectic diffeomorphisms.
机译：在二维维流形上，有一个C〜1残差（贝叶尔第二类）子态R，子集d≥1，因此对于R中的每个非Anosov f，其拓扑熵都受R的上界限制。 L的双曲周期点的李雅普诺夫指数在f的牢不可破的中心子束中（即，中心方向无支配分裂）。先前的结果涉及以下事实：对于辛微分态的C〜1残差集合R中的f（包含R）满足三分法：或者f是Anosov或f是具有稳健的维数为2m的稳固传递部分双曲型，0 < m

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