1 - Adapted metrics for codimension one singular hyperbolic flows
Luciana Salgado e Vinicius Coelho
ABSTRACT: We extend the three-dimensional result about Singular adapted metrics from Araujo-Salgado - Dominated splittings for exterior powers and singular hyperbolicity - for codimension one flows.
2 - Lyapunov functions, strong homogeneous sets and star flows (last version from 2016 - submitted)
Luciana Salgado
ABSTRACT:We say that a flow or vector field X ∈ X^1(M) is star on a compact invariant set L if there exist neighborhoods U of X and V of L for which every closed orbit in V of every vector field Y in U is hyperbolic. In this work, it is presented a characterization of star condition for flows based on Lyapunov functions. It is obtained conditions to strong homogeneity for singular sets for a C^1 flow by using the notion of infinitesimal Lyapunov functions. As an
application we obtain some results related to singular hyperbolic sets for flows.