Stability of closed characteristics on compact convex hypersurfaces in ℝ6
نویسندگان
چکیده
منابع مشابه
Stability of closed characteristics on compact convex hypersurfaces in R
In this paper, let Σ ⊂ R be a compact convex hypersurface. We prove that if Σ carries only finitely many geometrically distinct closed characteristics, then at least two of them must possess irrational mean indices. Moreover, if Σ carries exactly three geometrically distinct closed characteristics, then at least two of them must be elliptic.
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For any given compact C2 hypersurface Σ in R2n bounding a strictly convex set with nonempty interior, in this paper an invariant ̺n(Σ) is defined and satisfies ̺n(Σ) ≥ [n/2] + 1, where [a] denotes the greatest integer which is not greater than a ∈ R. The following results are proved in this paper. There always exist at least ̺n(Σ) geometrically distinct closed characteristics on Σ. If all the geom...
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There is a long standing conjecture in Hamiltonian analysis which claims that there exist at least n geometrically distinct closed characteristics on every compact convex hypersurface in R with n ≥ 2. Besides many partial results, this conjecture has been only completely solved for n = 2. In this paper, we give a confirmed answer to this conjecture for n = 3. In order to prove this result, we e...
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There is a long standing conjecture in Hamiltonian analysis which claims that there exist at least n geometrically distinct closed characteristics on every compact convex hypersurface in R with n ≥ 2. Besides many partial results, this conjecture has been only completely solved for n = 2. In this paper, we give a confirmed answer to this conjecture for n = 3. In order to prove this result, we e...
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ژورنال
عنوان ژورنال: Journal of the European Mathematical Society
سال: 2009
ISSN: 1435-9855
DOI: 10.4171/jems/161