A dichotomy result for closed characteristics on compact star-shaped hypersurfaces in $\mathbf{R}^{2n}$
Symplectic Geometry
2022-05-31 v1 Dynamical Systems
Abstract
In this paper, we prove that if all closed characteristics on a compact non-degenerate star-shaped hypersurface in are elliptic, then either there exist exactly geometrically distinct closed characteristics, or there exist infinitely many geometrically distinct closed characteristics.
Keywords
Cite
@article{arxiv.2205.14789,
title = {A dichotomy result for closed characteristics on compact star-shaped hypersurfaces in $\mathbf{R}^{2n}$},
author = {Huagui Duan and Hui Liu and Wenyan Ren},
journal= {arXiv preprint arXiv:2205.14789},
year = {2022}
}
Comments
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