Article Contents
Article Contents

# Sectional-hyperbolic Lyapunov stable sets

The first author is supported by UNAL from Colombia. The second author is supported by COLCIENCIAS and UNAL from Colombia

• 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 $X$.

Mathematics Subject Classification: Primary: 37D30; Secondary: 37D99.

 Citation:

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