Closed characteristics on compact convex hypersurfaces in $\R^{2n}$
| dc.creator | Long, Yiming | |
| dc.creator | Zhu, Chaofeng | |
| dc.date | 2001-09-18 | |
| dc.date | 2004-05-25 | |
| dc.date.accessioned | 2026-07-07T04:43:25Z | |
| dc.date.available | 2026-07-07T04:43:25Z | |
| dc.description | For any given compact C^2 hypersurface Σin {\bf R}^{2n} bounding a strictly convex set with nonempty interior, in this paper an invariant \varrho_n(Σ) is defined and satisfies \varrho_n(Σ)\ge [n/2]+1, where [a] denotes the greatest integer which is not greater than a\in {\bf R}. The following results are proved in this paper. There always exist at least ρ_n(Σ) geometrically distinct closed characteristics on Σ. If all the geometrically distinct closed characteristics on Σare nondegenerate, then \varrho_n(Σ)\ge n. If the total number of geometrically distinct closed characteristics on Σis finite, there exists at least an elliptic one among them, and there exist at least \varrho_n(Σ)-1 of them possessing irrational mean indices. If this total number is at most 2\varrho_n(Σ) -2, there exist at least two elliptic ones among them. | |
| dc.description | 52 pages, published version | |
| dc.identifier | https://arxiv.org/abs/math/0109116 | |
| dc.identifier | http://arxiv.org/abs/math/0109116 | |
| dc.identifier | Ann. of Math. (2), Vol. 155 (2002), no. 2, 317--368 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62214 | |
| dc.subject | Dynamical Systems | |
| dc.subject | Symplectic Geometry | |
| dc.subject | 58E05 | |
| dc.title | Closed characteristics on compact convex hypersurfaces in $\R^{2n}$ | |
| dc.type | text |