Sectional-hyperbolic lyapunov stable sets
Dynamical Systems
2018-04-05 v1
Abstract
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.
Cite
@article{arxiv.1804.01412,
title = {Sectional-hyperbolic lyapunov stable sets},
author = {Serafin Bautista and Yeison Sánchez},
journal= {arXiv preprint arXiv:1804.01412},
year = {2018}
}
Comments
arXiv admin note: text overlap with arXiv:1804.00646