16 citations · 40 across the 7 of their papers we have counts for
8 papers
A link between Topological Entropy and Lyapunov Exponents
Thiago Catalan
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 i…
On m-minimal partially hyperbolic diffeomorphisms
Alexander Arbieto, Thiago Catalan, Felipe Nobili
We discuss about the denseness of the strong stable and unstable manifolds of partially hyperbolic diffeomorphisms. In this sense, we introduce a concept of m-minimality. More prec…
Mixing-like properties for some generic and robust dynamics
Alexander Arbieto, Thiago Catalan, Bruno Santiago
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 suppo…
-Genericity of Symplectic Diffeomorphisms and Lower Bounds for Topological Entropy
Thiago Catalan, Vanderlei Horita
There is a -residual (Baire second class) subset of symplectic diffeomorphisms on -dimensional manifold, , such that for every non-Anosov in $\m…
Symbolic Extensions and dominated splittings for Generic C^1-Diffeomorphisms
A. Arbieto, A. Armijo, T. Catalan +1
Let Diff^1(M) be the set of all C^1-diffeomorphisms f : M \rightarrow M, where M is a compact boundaryless d-dimensional manifold, d \geq 2. We prove that there is a residual subse…
A C1 generic condition for existence of symbolic extensions of volume preserving diffeomorphisms
Thiago Catalan
We prove that a C1-generic volume preserving diffeomorphism has a symbolic extension if and only if this diffeomorphism is partial hyperbolic. This result is obtained by means of g…
A lower bound for topological entropy of generic non Anosov symplectic diffeomorphisms
Thiago Catalan, Ali Tahzibi
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 expone…
Hyperbolicity in the Volume Preserving Scenario
Alexander Arbieto, Thiago Catalan
Hayashi has extended a result of Mañé, proving that every diffeomorphism which has a -neighborhood , where all periodic points of any are hy…