On symplectic transformations of linear Hamiltonian differential systems without normality (Q518467)
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scientific article; zbMATH DE number 6697789
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| English | On symplectic transformations of linear Hamiltonian differential systems without normality |
scientific article; zbMATH DE number 6697789 |
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On symplectic transformations of linear Hamiltonian differential systems without normality (English)
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28 March 2017
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In this note, the oscillations of conjoined bases of linear Hamiltonian differential systems related via symplectic transformations are investigated. The investigations started in [the author, J. Math. Anal. Appl. 444, No. 2, 1260--1273 (2016; Zbl 1356.34039)] are continued by applying the so-called comparative index to refine classical results of the oscillation theory of the considered linear Hamiltonian system. The main result of this paper (Theorem 2.1) generalizes Theorem 1 from [\textit{O. Došlý}, Arch. Math., Brno 27b, 211--219 (1991; Zbl 0764.34026)].
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linear Hamiltonian differential systems
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transformation theory
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reciprocity principle
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comparative index
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