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Three closed characteristics on non-degenerate star-shaped hypersurfaces in $\mathbf{R}^{6}$

Huagui Duan, Hui Liu, Yiming Long, Zihao Qi, Wei Wang

Abstract

In this paper, we prove that for every non-degenerate $C^3$ compact star-shaped hypersurface $Σ$ in $\mathbf{R}^{6}$ which carries no prime closed characteristic of Maslov-type index $0$ or no prime closed characteristic of Maslov-type index $-1$, there exist at least three prime closed characteristics on $Σ$.

Three closed characteristics on non-degenerate star-shaped hypersurfaces in $\mathbf{R}^{6}$

Abstract

In this paper, we prove that for every non-degenerate compact star-shaped hypersurface in which carries no prime closed characteristic of Maslov-type index or no prime closed characteristic of Maslov-type index , there exist at least three prime closed characteristics on .
Paper Structure (4 sections, 129 equations)

This paper contains 4 sections, 129 equations.

Table of Contents

  1. Introduction and main results
  2. Critical point theory for closed characteristics on compact star-shaped hypersurfaces in ${\bf R}^{2n}$
  3. Index iteration theory for symplectic paths
  4. Proof of the main theorem