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

2001/09/20 by Viktor L. Ginzburg, Ginzburg, Viktor L., Başak Z. Gürel +2
Mathematics · #37J45 and 53D30 #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Symplectic Geometry (math.SG) #math.DG #math.DS #math.SG #msc:37J45 #msc:53D30

paper · pdf · doi:10.48550/arxiv.math/0109153

latex, 8 pages

arxiv created 2001/09/20 · openalex publication_date 2001/09/20 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We outline the construction of a proper C²-smooth function on R⁴ such that its Hamiltonian flow has no periodic orbits on at least one regular level set. This result can be viewed as a C²-smooth counterexample to the Hamiltonian Seifert conjecture in dimension four.

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