Email this article Symplectic geometry of a linear transformation with a quadratic invariant
- Authors: Kozlov V.V.1,2
-
Affiliations:
- Steklov Mathematical Institute
- RUDN University
- Issue: Vol 96, No 3 (2017)
- Pages: 625-627
- Section: Mathematics
- URL: https://journals.rcsi.science/1064-5624/article/view/225434
- DOI: https://doi.org/10.1134/S1064562417060254
- ID: 225434
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Abstract
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.
About the authors
V. V. Kozlov
Steklov Mathematical Institute; RUDN University
Author for correspondence.
Email: kozlov@pran.ru
Russian Federation, Moscow, 119991; Moscow, 117198
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