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

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

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

Original language description

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.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

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Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2016

Confidentiality

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

Name of the periodical

Journal of Differential Equations

ISSN

0022-0396

e-ISSN

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Volume of the periodical

260

Issue of the periodical within the volume

8

Country of publishing house

US - UNITED STATES

Number of pages

23

Pages from-to

6581-6603

UT code for WoS article

000371450000006

EID of the result in the Scopus database

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