English

Lyapunov stability and sectional-hyperbolicity for higher-dimensional flows

Dynamical Systems 2012-01-09 v1

Abstract

We study C1C^1-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}.

Keywords

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

R2 v1 2026-06-21T20:01:24.416Z