Closed characteristics on compact convex hypersurfaces in $\R^{2n}$

dc.creatorLong, Yiming
dc.creatorZhu, Chaofeng
dc.date2001-09-18
dc.date2004-05-25
dc.date.accessioned2026-07-07T04:43:25Z
dc.date.available2026-07-07T04:43:25Z
dc.descriptionFor 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.description52 pages, published version
dc.identifierhttps://arxiv.org/abs/math/0109116
dc.identifierhttp://arxiv.org/abs/math/0109116
dc.identifierAnn. of Math. (2), Vol. 155 (2002), no. 2, 317--368
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/62214
dc.subjectDynamical Systems
dc.subjectSymplectic Geometry
dc.subject58E05
dc.titleClosed characteristics on compact convex hypersurfaces in $\R^{2n}$
dc.typetext

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