Geodesic
Counterexamples to the Seifert conjecture
Documenta mathematica, ICM Berlin 1998, Vol. II (1998), pp. 831-840.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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.
Classification : 37C10, 37C85
Keywords: 3-dimensional sphere $S^3$, Hopf fibration, aperiodic vector fields on $S^3$, periodic orbits, dynamical system, plug, minimal set, PL foliation 
@article{DOCMA_1998__S8__a3,
     author = {Kuperberg, Krystyna},
     title = {Counterexamples to the {Seifert} conjecture},
     journal = {Documenta mathematica},
     pages = {831--840},
     publisher = {mathdoc},
     volume = {ICM Berlin 1998, Vol. II},
     year = {1998},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_1998__S8__a3/}
}
TY  - JOUR
AU  - Kuperberg, Krystyna
TI  - Counterexamples to the Seifert conjecture
JO  - Documenta mathematica
PY  - 1998
SP  - 831
EP  - 840
VL  - ICM Berlin 1998, Vol. II
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DOCMA_1998__S8__a3/
LA  - en
ID  - DOCMA_1998__S8__a3
ER  - 
%0 Journal Article
%A Kuperberg, Krystyna
%T Counterexamples to the Seifert conjecture
%J Documenta mathematica
%D 1998
%P 831-840
%V ICM Berlin 1998, Vol. II
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DOCMA_1998__S8__a3/
%G en
%F DOCMA_1998__S8__a3
Kuperberg, Krystyna. Counterexamples to the Seifert conjecture. Documenta mathematica, ICM Berlin 1998, Vol. II (1998), pp. 831-840. http://geodesic.mathdoc.fr/item/DOCMA_1998__S8__a3/