Geodesic
A $C^2$-smooth counterexample to the Hamiltonian Seifert conjecture in $\mathbb{R}^4$
Viktor L. Ginzburg1 ; Başak Gürel2
1 Department of Mathematics, University of California Santa Cruz, Santa Cruz, CA 95064, United States
2 Department of Mathematics, SUNY at Stony Brook, Stony Brook, NY 11794, United States
Annals of mathematics, Tome 158 (2003) no. 3, pp. 953-976.

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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.
DOI : 10.4007/annals.2003.158.953

Viktor L. Ginzburg 1 ; Başak Gürel 2

1 Department of Mathematics, University of California Santa Cruz, Santa Cruz, CA 95064, United States
2 Department of Mathematics, SUNY at Stony Brook, Stony Brook, NY 11794, United States 
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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. http://geodesic.mathdoc.fr/articles/10.4007/annals.2003.158.953/

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