Genera of Conjoined Bases for (Non)oscillatory Linear Hamiltonian Systems: Extended Theory
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F20%3A00114315" target="_blank" >RIV/00216224:14310/20:00114315 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s10884-019-09810-w" target="_blank" >https://doi.org/10.1007/s10884-019-09810-w</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10884-019-09810-w" target="_blank" >10.1007/s10884-019-09810-w</a>
Alternative languages
Result language
angličtina
Original language name
Genera of Conjoined Bases for (Non)oscillatory Linear Hamiltonian Systems: Extended Theory
Original language description
In this paper we study the properties of conjoined bases of a general linear Hamiltonian system without any controllability condition. When the Legendre condition holds and the system is nonoscillatory, it is known from our previous work that conjoined bases with eventually the same image form a special structure called a genus. In this work we extend the theory of genera of conjoined bases to arbitrary systems, for which the Legendre condition is not assumed and/or the system may be oscillatory. We derive a classification of all genera of conjoined bases and show that they form a complete lattice. These results are based on the relationship between subspaces of solutions of a linear control system and orthogonal projectors satisfying a certain Riccati type differential equation. The presented theory is applied in our paper (Sepitka in Discrete Contin Dyn Syst 39(4):1685-1730,2019) to general Riccati matrix differential equations for possibly uncontrollable linear Hamiltonian systems.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of dynamics and differential equations.
ISSN
1040-7294
e-ISSN
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Volume of the periodical
32
Issue of the periodical within the volume
3
Country of publishing house
US - UNITED STATES
Number of pages
17
Pages from-to
1139-1155
UT code for WoS article
000541929200001
EID of the result in the Scopus database
2-s2.0-85075386742