Sectional-hyperbolic lyapunov stable sets

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 s...

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Bibliographic Details
Published in:arXiv.org 2018-04
Main Authors: Bautista, Serafin, Sánchez, Yeison
Format: Article
Language:English
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Fields (mathematics)
Online Access:Get full text
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Summary: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.
ISSN:2331-8422