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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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