2018/04/03 by Bautista, Serafin, Sánchez, Yeison
#Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.1804.01412
In hyperbolic dynamics, a well-known result is: every hyperbolic Lyapunov stable set, is attracting; it's natural to wonder if this result is maintained in the sectional-hyperbolic dynamics. This question is still open, although some partial results have been presented. We will prove that all sectional-hyperbolic transitive Lyapunov stable set of codimension one of a vector field X over a compact manifold, with unique singularity Lorenz-like, which is of boundary-type, is an attractor of X.