11 research outputs found
A lower bound for topological entropy of generic non Anosov symplectic diffeomorphisms
We prove that a generic symplectic diffeomorphism is either Anosov or
the topological entropy is bounded from below by the supremum over the smallest
positive Lyapunov exponent of the periodic points. We also prove that
generic symplectic diffeomorphisms outside the Anosov ones do not admit
symbolic extension and finally we give examples of volume preserving
diffeomorphisms which are not point of upper semicontinuity of entropy function
in topology
Mixing-like properties for some generic and robust dynamics
We show that the set of Bernoulli measures of an isolated topologically
mixing homoclinic class of a generic diffeomorphism is a dense subset of the
set of invariant measures supported on the class. For this, we introduce the
large periods property and show that this is a robust property for these
classes. We also show that the whole manifold is a homoclinic class for an open
and dense subset of the set of robustly transitive diffeomorphisms far away
from homoclinic tangencies. In particular, using results from Abdenur and
Crovisier, we obtain that every diffeomorphism in this subset is robustly
topologically mixing
Lower bounds for entropy, symbolic extensions and hyperbolicity in the symplectic and volume preserving scenario
Provamos que \'C POT. 1\' genericamente difeomorfismos simpléticos ou são Anosov ou possuem entropia topológica limitada por baixo pelo supremo sobre o menor expoente de Lyapunov positivo dos pontos periódicos hiperbólicos. Usando isto exibimos exemplos de difeomorfismos conservativos sobre superfícies que não são pontos de semicontinuidade superior para a entropia topológica. Provamos também que \'C POT. 1\' genericamente difeomorfismos simpléticos não Anosov não admitem extensões simbólicas. Mudando de assunto, Hayashi estendeu um resultado de Mañé, provando que todo difeomorfismo f que possui uma \'C POT. 1\' vizinhança U, onde todos os pontos periódicos de qualquer g \'PERTENCE A\' U são hiperbólicos, é de fato um difeomorfismo Axioma A. Aqui, provamos o resultado análogo a este no caso conservativo, e a partir deste é possível exibir uma demonstração de um fato \"folclore\", a conjectura de Palis no caso conservativoWe prove that a \'C POT.1\' generic symplectic diffeomorphism is either Anosov or the topological entropy is bounded from below by the supremum over the smallest positive Lyapunov exponent of the periodic points. By means of that we give examples of area preserving diffeomorphisms which are not point of upper semicontinuity of entropy function in \'C POT. 1\' topology. We also prove that \'C POT. 1\'- generic symplectic diffeomorphisms outside the Anosov ones do not admit symbolic extension. Changing of subject, Hayashi has extended a result of Mañé, proving that every diffeomorphism f which has a \'C POT. 1\'-neighborhood U, where all periodic points of any g \'IT BELONGS\' U are hyperbolic, it is an Axiom A diffeomorphism. Here, we prove the analogous result in the volume preserving scenario, and using it we prove a \"folklore\" fact, the Palis conjecture in this contex
Generic properties about entropy and Hausdorff dimensions for area preserving diffeomorphisms of surfaces
Apresentamos duas propriedades genéricas para difeomorfismos conservativos da classe \'C POT.1\' sobre uma superfície compacta de dimensão dois. Obtemos uma limitação inferior para entropia topológica de difeomorfismos genéricos, e mostramos que tais difeomorfismos sempre possuem conjuntos invariantes fechados com órbitas densas e dimensão de Hausdorff doisWe present two generic properties of \'C POT.1\" area preserving diffeomorphisms of a two dimensional compact oriented surface. We obtain a lower bound for the topological entropy of a generic diffeomorphisms, and we show that such a diffeomorphism always has closed invariant sets with dense orbits and Hausdorff dimension tw