For a nonautonomous dynamics defined by a sequence of linear operators, we obtain a
complete characterization of the notion of a uniform exponential dichotomy in terms of the …

There are notions of singular hyperbolicity and sectional Lyapunov exponents of orders
beyond the classical ones, namely, other dimensions besides the dimension 2 and the full …

For a partially hyperbolic splitting T_ Γ M= E ⊕ F of Γ, a C^ 1 vector field X on am-manifold,
we obtain singular-hyperbolicity using only the tangent map DX of X and its derivative DX_ t …

Singular and sectional-hyperbolic sets are the objects of the extension of the classical
Smale Hyperbolic Theory to flows having invariant sets with singularities accumulated by …

For a partially hyperbolic splitting a $ C^ 1$ vector field $ X $ on a $ m $-manifold $ M $, we
obtain singular hyperbolicity whether $ E $ is one-dimensional subspace, based on the idea …

We show the existence of singular adapted metrics for any codimension one singular
hyperbolic set with respect to a C1 vector field on finite dimensional compact manifolds …

In this work, it is presented a characterization of star property for a C 1 vector field based on
Lyapunov functions. It is also obtained conditions to strong homogeneity for singular sets by …

We say that a flow or vector field X∈ X1 (M) is star if there exists a neighborhood U⊂ X1 (M)
of X for which every closed orbit of every vector field Y in U is hyperbolic. In this work, it is …