On the construction of a $C^2$-counterexample to the Hamiltonian Seifert Conjecture in $\mathbb{R}^4$

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On the construction of a $C^2$-counterexample to the Hamiltonian Seifert Conjecture in $\mathbb{R}^4$

Viktor L. Ginzburg and Basak Z. Gürel

Abstract.

We outline the construction of 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.

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Article Info

ERA Amer. Math. Soc. 08 (2002), pp. 11-19
Publisher Identifier: S 1079-6762(02)00100-2
2000 Mathematics Subject Classification. Primary 37J45; Secondary 53D30
Key words and phrases. Hamiltonian Seifert conjecture, periodic orbits
Received by the editors September 20, 2001
Posted on June 19, 2002
Communicated by Krystyna Kuperberg
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Viktor L. Ginzburg

Department of Mathematics, UC Santa Cruz, Santa Cruz, CA 95064, USA

E-mail address: ginzburg@math.ucsc.edu

Basak Z. Gürel

Department of Mathematics, UC Santa Cruz, Santa Cruz, CA 95064, USA

E-mail address: basak@math.ucsc.edu

The work is partially supported by the NSF and by the faculty research funds of the University of California, Santa Cruz.

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