Orthogonal-symplectic matrices and their parametric representation (Q6615402)
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scientific article; zbMATH DE number 7923131
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Orthogonal-symplectic matrices and their parametric representation |
scientific article; zbMATH DE number 7923131 |
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Orthogonal-symplectic matrices and their parametric representation (English)
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8 October 2024
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Based on previous results by the second author [Russ. Math. 64, No. 6, 80--85 (2020; Zbl 1460.37056); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2020, No. 6, 93--98 (2020)] the authors propose an algorithm for constructing any orthogonal symplectic matrix. For orders equal to \(2\), \(4\), \(6\), \(8\), they provide explicit forms for these matrices. From the obtained results it is possible to derive the dimension of the family of such matrices. Additionally, the authors employ the results to the study of periodic solutions of an autonomous Hamiltonian system with two degrees of freedom.
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orthogonal matrix
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symplectic matrix
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periodic solution
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Hamiltonian system
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monodromy matrix
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