Counterexamples to the Seifert conjecture (Q1126736)
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scientific article; zbMATH DE number 1184292
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Counterexamples to the Seifert conjecture |
scientific article; zbMATH DE number 1184292 |
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Counterexamples to the Seifert conjecture (English)
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6 August 1998
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Summary: Since H. Seifert proved in 1950 the existence of a periodic orbit for a vector field on the 3-dimensional sphere \(S^3\) which forms small angles with the fibers of the Hopf fibration, several examples of aperiodic vector fields on \(S^3\) have been produced as well as results showing that in some situations a compact orbit must exist. This paper surveys presently known types of vector fields without periodic orbits on \(S^3\) and on other manifolds.
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3-dimensional sphere \(S^3\)
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Hopf fibration
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aperiodic vector fields on \(S^3\)
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periodic orbits
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dynamical system
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plug
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minimal set
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PL foliation
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