A dichotomy result for closed characteristics on compact star-shaped hypersurfaces in $$\mathbf{R}^{2n}$$

• DOI: 10.1007/s00209-022-03085-6
• Publication Date: 2022-07-15T11:05:32Z
• Authors: Huagui Duan; Hui Liu; Wenyan Ren
• Keywords: Mathematics - Symplectic Geometry; 0103 physical sciences; FOS: Mathematics; Symplectic Geometry (math.SG); Dynamical Systems (math.DS); Mathematics - Dynamical Systems; 01 natural sciences

17 pages, to appear in Mathematische Zeitschrift. arXiv admin note: substantial text overlap with arXiv:2205.07082, arXiv:1510.08648, arXiv:1601.03470, arXiv:1405.5739, arXiv:1308.3904, arXiv:1308.3543<br/>In this paper, we prove that if all closed characteristics on a compact non-degenerate star-shaped hypersurface $Σ$ in $\mathbf{R}^{2n}$ are elliptic, then either there exist exactly $n$ geometrically distinct closed characteristics, or there exist infinitely many geometrically distinct closed characteristics.<br/>