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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.

*Copyright 2002 American Mathematical Society*

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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
- Comments (When Available)

**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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