Symplectic geometry of a linear transformation with a quadratic invariant

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作者：
V. V. Kozlov
机构：
[1] Russian Academy of Sciences,Steklov Mathematical Institute
[2] RUDN University,undefined
来源：
Doklady Mathematics | 2017年 / 96卷
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摘要：
A linear transformation with an invariant being a nondegenerate quadratic form is symplectic. The geometric properties of such transformations are discussed. A complete set of quadratic invariants which are pairwise in involution is explicitly specified. The structure of the isotropic cone on which all these integrals simultaneously vanish is investigated. Applications of the general results to the problem on the stability of a fixed point of a linear transformation with a quadratic invariant are discussed.
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页码：625 / 627
页数：2
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