Seifert conjecture in the even convex case

Chungen Liu; Duanzhi Zhang

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arXiv · 1303.6752

Seifert conjecture in the even convex case

Chungen Liu·Duanzhi Zhang

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Abstract

In this paper, we prove that there exist at least $n$ geometrically distinct brake orbits on every $C^2$ compact convex symmetric hypersurface $\Sg$ in $\R^{2n}$ satisfying the reversible condition $N\Sg=\Sg$ 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 $n$.

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Chungen Liu, Duanzhi Zhang. 2013-03-27. Seifert conjecture in the even convex case. https://arxiv.org/abs/1303.6752

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