Hamilton-Arnold Chord And Seifert Conjecture

Details Hamilton-Arnold Chord And Seifert Conjecture Hamilton-Arnold Chord And Seifert Conjecture

2006-03-13

arxiv.org/abs/math/0603282v2

Mathematics

Symplectic Geometry

Scientific paper

In this article, we prove that there exists at least one chord orbit of Hamilton vector field connecting the Legendre submanifold on a given energy hypersurface in some symplectic manifolds. As an application, we prove that there exists at least one periodic orbit of Hamilton vector field on a given energy hypersurface in $R^{2n}$ which proves the longstanding Seifert's conjecture. The more general results are also obtained.

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