On critical orbits and sectional hyperbolicity of the nonwandering set for flows

In this note, we introduce the notion of nonuniformly sectional hyperbolic set and use it to prove that any C1-open set which contains a residual subset of vector fields with nonuniformly sectional hyperbolic critical set also contains a residual subset of vector fields with sectional hyperbolic nonwandering set. This not only extends Theorem A of Castro [11], but using suspensions we recover it.