Riccati equations for linear Hamiltonian systems without controllability condition

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F19%3A00107305" target="_blank" >RIV/00216224:14310/19:00107305 - isvavai.cz</a>
Result on the web
<a href="https://www.aimsciences.org/article/doi/10.3934/dcds.2019074" target="_blank" >https://www.aimsciences.org/article/doi/10.3934/dcds.2019074</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3934/dcds.2019074" target="_blank" >10.3934/dcds.2019074</a>

Result language
angličtina
Original language name
Riccati equations for linear Hamiltonian systems without controllability condition
Original language description
In this paper we develop new theory of Riccati matrix differential equations for linear Hamiltonian systems, which do not require any controllability assumption. When the system is nonoscillatory, it is known from our previous work that conjoined bases of the system with eventually the same image form a special structure called a genus. We show that for every such a genus there is an associated Riccati equation. We study the properties of symmetric solutions of these Riccati equations and their connection with conjoined bases of the system. For a given genus, we pay a special attention to distinguished solutions at infinity of the associated Riccati equation and their relationship with the principal solutions at infinity of the system in the considered genus. We show the uniqueness of the distinguished solution at infinity of the Riccati equation corresponding to the minimal genus. This study essentially extends and completes the work of W. T. Reid (1964, 1972), W. A. Coppel (1971), P. Hartman (1964), W. Kratz (1995), and other authors who considered the Riccati equation and its distinguished solution at infinity for invertible conjoined bases, i.e., for the maximal genus in our setting.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA16-00611S" target="_blank" >GA16-00611S: Hamiltonian and symplectic systems: oscillation and spectral theory</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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