Hamilton-Arnold Chord And Periodic Orbits

Abstract

In this article, we first prove that every Hamilton flow has at least as many Hamilton- Arnold chords as a smooth function on the Legendre submanifold of zero first cohomology has critical points. Second, we prove that every Hamilton flow has at least as many close Hamilton orbits as a smooth round function on the close Hamilton manifold of zero first cohomology has critical circles which implies that the so called Arnold-Ginzburg or Seifert conjecture holds.