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

Abstract

In this paper, we prove that for every non-degenerate $C^3$ compact star-shaped hypersurface $\hat{I}\pounds$ 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 $\hat{I}\pounds$.

30 pages. arXiv admin note: text overlap with arXiv:2205.07082, arXiv:1510.08648, arXiv:2205.14789