2000
DOI: 10.1006/aima.2000.1914
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Precise Iteration Formulae of the Maslov-type Index Theory and Ellipticity of Closed Characteristics

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Cited by 114 publications
(149 citation statements)
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References 36 publications
(47 reference statements)
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“…Motivated by these results and conjectures, we confirm the symmetry conjecture for the case n = 4 when #J ( ) = 4: Theorem 1.1 For every ∈ SH (8) satisfying #J ( ) = 4, all the closed characteristics on are symmetric.…”
Section: -Action Is Defined By θ · Y(t) = Y(t + τ θ) ∀θ ∈ S 1 T ∈ supporting
confidence: 63%
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“…Motivated by these results and conjectures, we confirm the symmetry conjecture for the case n = 4 when #J ( ) = 4: Theorem 1.1 For every ∈ SH (8) satisfying #J ( ) = 4, all the closed characteristics on are symmetric.…”
Section: -Action Is Defined By θ · Y(t) = Y(t + τ θ) ∀θ ∈ S 1 T ∈ supporting
confidence: 63%
“…In Sect. 3, we prove the main result using equivariant Morse theory, index iteration theory developed by Long and his coworkers, especially the common index jump theorem of Long and Zhu, and a commutative property for closed characteristics in the common index jump intervals discovered by Wang in [16] which played a crucial role in his proof of the existence of four geometrically distinct closed characteristics on every compact convex hypersurface in R 8 . Note that this commutative property was also used in [17].…”
Section: -Action Is Defined By θ · Y(t) = Y(t + τ θ) ∀θ ∈ S 1 T ∈ mentioning
confidence: 82%
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“…In [L-Z], they proved that any such hypersurface carries at least [n/2] + 1 closed trajectories, while in [L-L-Z], they show that there are at least n if, in addition, one assumes symmetry of the surface around the origin. Unfortunately, we cannot go into the proofs of these beautiful results here and the reader is referred to [E2], [Lo1] and [Lo2] for that story. Instead, we present a very simple example to illustrate the use of Theorem 5.1.…”
Section: Morse Indices Of Variationally Generated Critical Pointsmentioning
confidence: 99%