171:
counterexample. Later this construction was shown to have real analytic and piecewise linear versions. In 1997 for the particular case of incompressible fluids it was shown that all
36:. In a 1950 paper, Seifert asked if such a vector field exists, but did not phrase non-existence as a conjecture. He also established the conjecture for perturbations of the
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Ginzburg, Viktor L.; Gurel, Basak Z. (2001). "A C-smooth counterexample to the
Hamiltonian Seifert conjecture in R".
559:
Schweitzer, Paul A. (1974). "Counterexamples to the
Seifert Conjecture and Opening Closed Leaves of Foliations".
812:
807:
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273:"Pseudoholomorphic curves in symplectizations with applications to the Weinstein conjecture in dimension three"
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Seifert, Herbert (1950). "Closed
Integral Curves in 3-Space and Isotopic Two-Dimensional Deformations".
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140:. The existence of smoother counterexamples remained an open question until 1993 when
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404:(1996). "A volume-preserving counterexample to the Seifert conjecture".
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Etnyre, J.; Ghrist, R. (1997). "Contact
Topology and Hydrodynamics".
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460:(1996). "Generalized counterexamples to the Seifert conjecture".
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counterexample. Schweitzer's construction was then modified by
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520:(1994). "A smooth counterexample to the Seifert conjecture".
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possess closed flowlines based on similar results for
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24:states that every nonsingular, continuous
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32:has a closed orbit. It is named after
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144:constructed a very different
104:{\displaystyle C^{2+\delta }}
627:Kuperberg, Krystyna (1999).
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133:{\displaystyle \delta >0}
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191:{\displaystyle C^{\omega }}
164:{\displaystyle C^{\infty }}
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198:steady state flows on
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813:Disproved conjectures
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707:Euler's sum of powers
561:Annals of Mathematics
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463:Annals of Mathematics
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363:{\displaystyle C^{2}}
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637:Notices of the AMS
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297:10.1007/BF01232679
271:Hofer, H. (1993).
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22:Seifert conjecture
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466:. Second series.
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802:Categories
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782:Weyl–Berry
762:Schoen–Yau
679:Disproved
237:References
343:(1988). "
313:123618375
305:0020-9910
184:ω
157:∞
122:δ
114:for some
97:δ
757:Ragsdale
737:Keller's
732:Kalman's
692:Borsuk's
510:16309410
446:18212778
373:Topology
30:3-sphere
767:Seifert
742:Mertens
610:2032372
581:1971077
552:1307902
544:2118623
502:1394969
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285:Bibcode
229:on the
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490:JSTOR
472:arXiv
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416:arXiv
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