The study of hyperbolic structures (uniform and nonuniform ones)
is a central subject in Dynamical Systems.
Nowadays, there are many notions of weak hyperbolicity, and
here I am interested in the setting of flows with singularities (e.g.,
Lorenz systems).
In this talk I am going to talk about some notions of (nonuniform)
sectional hyperbolicity (in the sense of p-planes expansion) for C1 flows.And, how to use of the powerful tool of quadratic forms (Lyapunov Functions) to characterize dynamical properties and to obtain ergodic features for those kind of systems.
Finally, if time permits, I will state some new result involving
SRB measures for it, in a joint work with V. Aráujo (UFBA,
Brazil) and Sergio Sousa (UFRJ, Brazil).