Bifurcation and non-bifurcation of compact orbits by change of stability behavior (Q2266503)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Bifurcation and non-bifurcation of compact orbits by change of stability behavior |
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Bifurcation and non-bifurcation of compact orbits by change of stability behavior (English)
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1985
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Does the change of topological stability behavior as in Hopf bifurcation imply the bifurcation of compact orbits? It is shown that the answer is yes if the dimension of the phase space is odd or equals 2. For \(n\geq 4\), n even, counter-examples are exhibited.
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stationary point
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closed orbit
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asymptotic stability
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Poincaré-Hopf Theorem
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Poincaré-Bendixson Theorem
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Seifert Conjecture
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Hopf bifurcation
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