Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Closed Reeb orbits on contact type hypersurfaces in $T^*S^n$

Huagui Duan, Zihao Qi

Abstract

In this paper, it is proved that under dynamically convex condition, there exist at least $[\frac{n+1}{2}]$ closed Reeb orbits on a closed contact type hypersurface in $T^*S^n$ enclosing the zero section and bounding a simply connected Liouville domain. Furthermore, if the contact form is non-degenerate and has finitely many closed Reeb orbits, then there exist at least two irrationally elliptic closed Reeb orbits.

Closed Reeb orbits on contact type hypersurfaces in $T^*S^n$

Abstract

In this paper, it is proved that under dynamically convex condition, there exist at least closed Reeb orbits on a closed contact type hypersurface in enclosing the zero section and bounding a simply connected Liouville domain. Furthermore, if the contact form is non-degenerate and has finitely many closed Reeb orbits, then there exist at least two irrationally elliptic closed Reeb orbits.
Paper Structure (6 sections, 53 equations)

This paper contains 6 sections, 53 equations.

Table of Contents

  1. Introduction and main result
  2. Equivariant symplectic homology
  3. Maslov-type index for symplectic paths
  4. Proof of Main Theorems
  5. Proof of Theorem 1.1.
  6. Proof of Theorem 1.3.

Theorems & Definitions (2)

  • proof
  • proof