On the construction of a 𝐶²-counterexample to the Hamiltonian Seifert Conjecture in ℝ⁴

Ginzburg, Viktor; Gürel, Başak

doi:10.1090/S1079-6762-02-00100-2

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

Authors: Viktor L. Ginzburg and Başak Z. Gürel
Journal: Electron. Res. Announc. Amer. Math. Soc. 8 (2002), 11-19
MSC (2000): Primary 37J45; Secondary 53D30
DOI: https://doi.org/10.1090/S1079-6762-02-00100-2
Published electronically: June 19, 2002
MathSciNet review: 1911741
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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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