Lyapunov stability and sectional-hyperbolicity for higher-dimensional flows
Dynamical Systems
2012-01-09 v1
Abstract
We study -generic vector fields on closed manifolds without points accumulated by periodic orbits of different indices and prove that they exhibit finitely many sinks and sectional-hyperbolic transitive Lyapunov stable sets with residual basin of attraction. This represents a partial positive answer to conjectures in \cite{am}, the Palis conjecture \cite{pa} and extend the Araujo's thesis to higher dimensions \cite{a}.
Cite
@article{arxiv.1201.1464,
title = {Lyapunov stability and sectional-hyperbolicity for higher-dimensional flows},
author = {A. Arbieto and C. A. Morales and B. Santiago},
journal= {arXiv preprint arXiv:1201.1464},
year = {2012}
}
Comments
8 pages