Sectional-hyperbolic Lyapunov stable sets

Serafin Bautista; Yeison Sánchez

doi:10.3934/dcds.2020103

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2020, Volume 40, Issue 4: 2011-2016. Doi: 10.3934/dcds.2020103

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Sectional-hyperbolic Lyapunov stable sets

Serafin Bautista^, and
Yeison Sánchez

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

^* Corresponding author: sbautistad@unal.edu.co
^* Corresponding author: sbautistad@unal.edu.co

Received: March 31, 2018

Revised: July 31, 2019

Published: December 2019

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

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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 $.

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

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References

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