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

Author(s): Viktor L. Ginzburg; Basak Z. Gürel
Journal: Electron. Res. Announc. Amer. Math. Soc. 8 (2002), 11-19.
MSC (2000): Primary 37J45; Secondary 53D30
Posted: June 19, 2002
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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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Additional Information:

Viktor L. Ginzburg
Affiliation: Department of Mathematics, UC Santa Cruz, Santa Cruz, CA 95064, USA
Email: ginzburg@math.ucsc.edu

Basak Z. Gürel
Affiliation: Department of Mathematics, UC Santa Cruz, Santa Cruz, CA 95064, USA
Email: basak@math.ucsc.edu

DOI: 10.1090/S1079-6762-02-00100-2
PII: S 1079-6762(02)00100-2
Keywords: Hamiltonian Seifert conjecture, periodic orbits
Received by editor(s): September 20, 2001
Posted: June 19, 2002
Additional Notes: The work is partially supported by the NSF and by the faculty research funds of the University of California, Santa Cruz.
Communicated by: Krystyna Kuperberg
Copyright of article: Copyright 2002, American Mathematical Society

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