Genera of conjoined bases of linear Hamiltonian systems and limit characterization of principal solutions at infinity

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F16%3A00089253" target="_blank" >RIV/00216224:14310/16:00089253 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.jde.2016.01.004" target="_blank" >http://dx.doi.org/10.1016/j.jde.2016.01.004</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jde.2016.01.004" target="_blank" >10.1016/j.jde.2016.01.004</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Genera of conjoined bases of linear Hamiltonian systems and limit characterization of principal solutions at infinity

Popis výsledku v původním jazyce

In this paper we derive a general limit characterization of principal solutions at infinity of linear Hamiltonian systems under no controllability assumption. The main result is formulated in terms of a limit involving antiprincipal solutions at infinity of the system. The novelty lies in the fact that the principal and antiprincipal solutions at infinity may belong to two different genera of conjoined bases, i.e., the eventual image of their first components is not required to be the same as in the known literature. For this purpose we extend the theory of genera of conjoined bases, which was recently initiated by the authors. We show that the orthogonal projector representing each genus of conjoined bases satisfies a symmetric Riccati matrix differential equation. This result then leads to an exact description of the structure of the set of all genera, in particular it forms a complete lattice. We also provide several examples, which illustrate our new theory.

Název v anglickém jazyce

Genera of conjoined bases of linear Hamiltonian systems and limit characterization of principal solutions at infinity

Popis výsledku anglicky

In this paper we derive a general limit characterization of principal solutions at infinity of linear Hamiltonian systems under no controllability assumption. The main result is formulated in terms of a limit involving antiprincipal solutions at infinity of the system. The novelty lies in the fact that the principal and antiprincipal solutions at infinity may belong to two different genera of conjoined bases, i.e., the eventual image of their first components is not required to be the same as in the known literature. For this purpose we extend the theory of genera of conjoined bases, which was recently initiated by the authors. We show that the orthogonal projector representing each genus of conjoined bases satisfies a symmetric Riccati matrix differential equation. This result then leads to an exact description of the structure of the set of all genera, in particular it forms a complete lattice. We also provide several examples, which illustrate our new theory.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

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Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2016

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Differential Equations

ISSN

0022-0396

e-ISSN

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Svazek periodika

260

Číslo periodika v rámci svazku

8

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

23

Strana od-do

6581-6603

Kód UT WoS článku

000371450000006

EID výsledku v databázi Scopus

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