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- W1972981118 abstract "For any given compact C^2 hypersurface Sigma in {bf R}^{2n} bounding a strictly convex set with nonempty interior, in this paper an invariant varrho_n(Sigma) is defined and satisfies varrho_n(Sigma)ge [n/2]+1, where [a] denotes the greatest integer which is not greater than ain {bf R}. The following results are proved in this paper. There always exist at least rho_n(Sigma) geometrically distinct closed characteristics on Sigma. If all the geometrically distinct closed characteristics on Sigma are nondegenerate, then varrho_n(Sigma)ge n. If the total number of geometrically distinct closed characteristics on Sigma is finite, there exists at least an elliptic one among them, and there exist at least varrho_n(Sigma)-1 of them possessing irrational mean indices. If this total number is at most 2varrho_n(Sigma) -2, there exist at least two elliptic ones among them." @default.
- W1972981118 created "2016-06-24" @default.
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- W1972981118 date "2001-09-18" @default.
- W1972981118 modified "2023-10-16" @default.
- W1972981118 title "Closed characteristics on compact convex hypersurfaces in $R^{2n}$" @default.
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