# American Institute of Mathematical Sciences

April  2020, 40(4): 2011-2016. doi: 10.3934/dcds.2020103

## Sectional-hyperbolic Lyapunov stable sets

 Departamento de Matemáticas, Universidad Nacional de Colombia, Bogotá, Colombia

Received  April 2018 Revised  August 2019 Published  January 2020

Fund Project: 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 $X$.

Citation: Serafin Bautista, Yeison Sánchez. Sectional-hyperbolic Lyapunov stable sets. Discrete & Continuous Dynamical Systems - A, 2020, 40 (4) : 2011-2016. doi: 10.3934/dcds.2020103
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