C1-Genericity of symplectic diffeomorphisms and lower bounds for topological entropy

• Autor(a) principal: Catalan, Thiago
• Data de Publicação: 2017
• Outros Autores: Horita, Vanderlei [UNESP]
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://dx.doi.org/10.1080/14689367.2017.1278744; http://hdl.handle.net/11449/174128
• topic: elliptic periodic points; generic properties; homoclinic tangency; Partially hyperbolic symplectic systems; topological entropy

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.