A $C^2$-smooth counterexample to the Hamiltonian Seifert conjecture in $\mathbb{R}^4$
Annals of mathematics, Tome 158 (2003) no. 3, pp. 953-976
Voir la notice de l'article provenant de la source Annals of Mathematics website
We construct a proper $C^2$-smooth function on $\mathbb{R}^4$ such that its Hamiltonian flow has no periodic orbits on at least one regular level set. This result can be viewed as a $C^2$-smooth counterexample to the Hamiltonian Seifert conjecture in dimension four.
@article{10_4007_annals_2003_158_953,
author = {Viktor L. Ginzburg and Ba\c{s}ak G\"urel},
title = {A $C^2$-smooth counterexample to the {Hamiltonian} {Seifert} conjecture in $\mathbb{R}^4$},
journal = {Annals of mathematics},
pages = {953--976},
publisher = {mathdoc},
volume = {158},
number = {3},
year = {2003},
doi = {10.4007/annals.2003.158.953},
mrnumber = {2031857},
zbl = {1140.37356},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2003.158.953/}
}
TY - JOUR
AU - Viktor L. Ginzburg
AU - Başak Gürel
TI - A $C^2$-smooth counterexample to the Hamiltonian Seifert conjecture in $\mathbb{R}^4$
JO - Annals of mathematics
PY - 2003
SP - 953
EP - 976
VL - 158
IS - 3
PB - mathdoc
UR - http://geodesic.mathdoc.fr/articles/10.4007/annals.2003.158.953/
DO - 10.4007/annals.2003.158.953
LA - en
ID - 10_4007_annals_2003_158_953
ER -
%0 Journal Article
%A Viktor L. Ginzburg
%A Başak Gürel
%T A $C^2$-smooth counterexample to the Hamiltonian Seifert conjecture in $\mathbb{R}^4$
%J Annals of mathematics
%D 2003
%P 953-976
%V 158
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4007/annals.2003.158.953/
%R 10.4007/annals.2003.158.953
%G en
%F 10_4007_annals_2003_158_953
Viktor L. Ginzburg; Başak Gürel. A $C^2$-smooth counterexample to the Hamiltonian Seifert conjecture in $\mathbb{R}^4$. Annals of mathematics, Tome 158 (2003) no. 3, pp. 953-976. doi: 10.4007/annals.2003.158.953
Cité par Sources :