Reid roundabout theorem for symplectic dynamic systems on time scales
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F01%3A00008164" target="_blank" >RIV/00216224:14310/01:00008164 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
Reid roundabout theorem for symplectic dynamic systems on time scales
Original language description
The principal aim of this paper is to state and prove the so called Reid roundabout theorem for symplectic dynamic system (S) z<sup>Delta</sup>=S<sub>t</sub>z on an arbitrary time scale T, so that the well known case of differential linear Hamiltonian systems (T=R) and recently developed case of discrete symplectic systems (T=Z) are unified. We list conditions which are equivalent to the positivity of the quadratic functional associated with (S), e.g. disconjugacy (in terms of no focal points of a conjoined basis) of (S), no generalized zeros for vector solutions of (S), the existence of a solution to the corresponding Riccati matrix equation. A certain normality assumption is employed. The result requires treatment of the quadratic functionals both with general and separated boundary conditions.
Czech name
Reid roundabout theorem for symplectic dynamic systems on time scales
Czech description
The principal aim of this paper is to state and prove the so called Reid roundabout theorem for symplectic dynamic system (S) z<sup>Delta</sup>=S<sub>t</sub>z on an arbitrary time scale T, so that the well known case of differential linear Hamiltonian systems (T=R) and recently developed case of discrete symplectic systems (T=Z) are unified. We list conditions which are equivalent to the positivity of the quadratic functional associated with (S), e.g. disconjugacy (in terms of no focal points of a conjoined basis) of (S), no generalized zeros for vector solutions of (S), the existence of a solution to the corresponding Riccati matrix equation. A certain normality assumption is employed. The result requires treatment of the quadratic functionals both with general and separated boundary conditions.
Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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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
2001
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Applied Mathematics and Optimization
ISSN
0095-4616
e-ISSN
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Volume of the periodical
43
Issue of the periodical within the volume
2
Country of publishing house
US - UNITED STATES
Number of pages
18
Pages from-to
129-146
UT code for WoS article
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EID of the result in the Scopus database
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