Arnold conjecture for surface homeomorphisms

The Arnold Chord Conjecture

Simple Braids for Surface Homeomorphisms

Let S be a compact, oriented surface with negative Euler characteristic and let f : S → S be a homeomorphism isotopic to the identity. If there exists a periodic orbit with a non-zero rotation vector (~ p, q), then there exists a simple braid with the same rotation vector.

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 ...

Recurrent Surface Homeomorphisms

An orientation-preserving recurrent homeomorphism of the twosphere which is not the identity is shown to admit exactly two fixed points. A recurrent homeomorphism of a compact surface with negative Euler characteristic is periodic.

A Proof On Arnold-Chekanov Conjecture

In this article, we give a proof on the Arnold-Chekanov Lagrangian intersection conjecture on the cotangent bundles and its generalizations.