Hamilton-Arnold Chord On Stable Hypersurface

Ju l 2 00 4 A Proof On Generalized Arnold ’ s Chord Conjecture On Cotangent Bundles ∗

In this article, we prove that there exists at least one chord which is characteristic of Reeb vector field connecting a given Legendre sub-manifold in a contact manifolds of induced type in the cotangent bundles of any smooth open manifolds which confirms the generalized Arnold conjecture in cotangent bundles.

On Existences Of Periodic Orbits For Hamilton Systems

In this article, we prove that either there exists at least one periodic orbit of Hamilton vector field on a given energy hypersurface in R 2n or there exist at least two periodic orbits on the near-by energy hypersurface in R. The more general results are also obtained.

A Proof on Arnold's Chord Conjecture on Cotangent Bundles *

In this article, we prove that there exists at least one chord which is characteristic of Reeb vector field connecting a given Legendre sub-manifold in a contact manifolds of induced type in the cotangent bundles of any smooth open manifolds which confirms the Arnold conjecture in cotangent bundles.

The Arnold Chord Conjecture

A Proof On Arnold Chord Conjecture

In this article, we first prove that there exists a smooth foliation near codimension one skeleton which is transversal to the Reeb vector field on the contact manifold. Second, we use it to prove that there exists a smooth Poincare section for the Legendre submanifold. Third, we give a proof on the Arnold chord conjecture which states that every Reeb flow has at least as many Reeb chords as a ...