On symplectic transformations of linear Hamiltonian differential systems without normality
| Autor: | Julia Elyseeva |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Pure mathematics
Rank (linear algebra) Applied Mathematics 010102 general mathematics 01 natural sciences Symplectic matrix Hamiltonian system 010101 applied mathematics Algebra Transformation matrix 0101 mathematics Symplectomorphism Mathematics::Symplectic Geometry Moment map Hamiltonian (control theory) Mathematics Symplectic geometry |
| Zdroj: | Applied Mathematics Letters. 68:33-39 |
| ISSN: | 0893-9659 |
| DOI: | 10.1016/j.aml.2016.12.012 |
| Popis: | In this paper we investigate oscillations of conjoined bases of linear Hamiltonian differential systems related via symplectic transformations. Both systems are considered without controllability (or normality) assumptions and under the Legendre condition for their Hamiltonians. The main result of the paper presents new explicit relations connecting the multiplicities of proper focal points of Y ( t ) and the transformed conjoined basis Y ( t ) = R − 1 ( t ) Y ( t ) , where the symplectic transformation matrix R ( t ) obeys some additional assumptions on the rank of its components. As consequences of the main result we formulate the generalized reciprocity principle for the Hamiltonian systems without normality. The main tool of the paper is the comparative index theory for discrete symplectic systems generalized to the continuous case. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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