A robustly chain transitive attractor with singularities of different indices (Q2841758)
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scientific article; zbMATH DE number 6192528
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A robustly chain transitive attractor with singularities of different indices |
scientific article; zbMATH DE number 6192528 |
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A robustly chain transitive attractor with singularities of different indices (English)
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30 July 2013
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singular attractor
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robustly chain transitive
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partially hyperbolic
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index
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The authors construct a \(C^1\)-open set in the space of smooth vector fields on a 4-manifold with the \(C^1\)-topology such that any vector field in this set has a robustly chain transitive attractor containing two hyperbolic rest points of different indices. It is also shown that, for any robust attractor having such properties, \(C^1\)-small perturbations create homoclinic tangencies and heterodimensional cycles associated to closed orbits belonging to the attractor.
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