Seifert Conjecture in the Even Convex Case

By Chun-gen Liu, Duanzhi Zhang. 2013

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In this paper, we prove that there exist at least n geometrically distinct brake orbits on every C2 compact convex symmetric hypersurface Σ in ℝ2n satisfying the reversible condition NΣ = Σ with N = diag(−In,In). As a consequence, we show that if the Hamiltonian function is convex and even, then Seifert conjecture of 1948 on the multiplicity of brake orbits holds for any positive integern. © 2014 Wiley Periodicals, Inc.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/67407c36eb8a89fb22e3fe331f0ed79ff30d62dc