Saddle-focus singular cycles and prevalence of hyperbolicity (Q1266334)
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scientific article; zbMATH DE number 1199911
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Saddle-focus singular cycles and prevalence of hyperbolicity |
scientific article; zbMATH DE number 1199911 |
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Saddle-focus singular cycles and prevalence of hyperbolicity (English)
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3 April 2000
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The main goal of this paper is to show that in the unfolding of a three-dimensional vector field having a saddle-focus singular cycle hyperbolicity is a prevalent phenomenon: that is, the set of parameters corresponding to Axiom A flows has full Lebesgue density at this bifurcation value. Here for the first time nontrivial hyperbolicity is proved for the maximal invariant set for a perturbation of a vector field with a cycle containing a saddle-focus singularity.
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unfolding
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vector field
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saddle-focus singular cycle
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hyperbolicity
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