Seifert Conjecture in the Even Convex Case | Zendy

Liu Chungen | Zendy; Zhang Duanzhi | Zendy

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Seifert Conjecture in the Even Convex Case

Author(s) -

Liu Chungen,

Zhang Duanzhi

Publication year - 2014

Publication title -

communications on pure and applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 3.12

H-Index - 115

eISSN - 1097-0312

pISSN - 0010-3640

DOI - 10.1002/cpa.21525

Subject(s) - hypersurface , mathematics , conjecture , regular polygon , multiplicity (mathematics) , combinatorics , convex function , brake , pure mathematics , mathematical analysis , geometry , materials science , metallurgy

In this paper, we prove that there exist at least n geometrically distinct brake orbits on every C 2 compact convex symmetric hypersurface Σ in ℝ 2n satisfying the reversible condition N Σ = Σ with N = diag(− I n , I n ). 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 integer n . © 2014 Wiley Periodicals, Inc.

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