A dichotomy for higher-dimensional flows (Q2839366)
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scientific article; zbMATH DE number 6184481
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A dichotomy for higher-dimensional flows |
scientific article; zbMATH DE number 6184481 |
Statements
A dichotomy for higher-dimensional flows (English)
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5 July 2013
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sectional-axiom A
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Morse index
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vector field
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For a \(C^1\)-generic vector field \(X\), the authors investigate the dichotomy that either \(X\) has a point lying in the closure of the union of the periodic orbits of different Morse indices, or \(X\) is sectional-Axiom \(A\). They prove the dichotomy under the condition that the singularities of \(X\) lying in the closure of the union of the periodic orbits have codimension one. With this condition, they also prove that a \(C^1\)-generic star flow with spectral decomposition is sectional-Axiom \(A\).
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