Focal points and principal solutions of linear Hamiltonian systems revisited

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F18%3A00100766" target="_blank" >RIV/00216224:14310/18:00100766 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.jde.2018.01.016" target="_blank" >http://dx.doi.org/10.1016/j.jde.2018.01.016</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jde.2018.01.016" target="_blank" >10.1016/j.jde.2018.01.016</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Focal points and principal solutions of linear Hamiltonian systems revisited

Popis výsledku v původním jazyce

In this paper we present a novel view on the principal (and antiprincipal) solutions of linear Hamiltonian systems, as well as on the focal points of their conjoined bases. We present a new and unified theory of principal (and antiprincipal) solutions at a finite point and at infinity, and apply it to obtain new representation of the multiplicities of right and left proper focal points of conjoined bases. We show that these multiplicities can be characterized by the abnormality of the system in a neighborhood of the given point and by the rank of the associated T-matrix from the theory of principal (and antiprincipal) solutions. We also derive some additional important results concerning the representation of T-matrices and associated normalized conjoined bases. The results in this paper are new even for completely controllable linear Hamiltonian systems. We also discuss other potential applications of our main results, in particular in the singular Sturmian theory.

Název v anglickém jazyce

Focal points and principal solutions of linear Hamiltonian systems revisited

Popis výsledku anglicky

In this paper we present a novel view on the principal (and antiprincipal) solutions of linear Hamiltonian systems, as well as on the focal points of their conjoined bases. We present a new and unified theory of principal (and antiprincipal) solutions at a finite point and at infinity, and apply it to obtain new representation of the multiplicities of right and left proper focal points of conjoined bases. We show that these multiplicities can be characterized by the abnormality of the system in a neighborhood of the given point and by the rank of the associated T-matrix from the theory of principal (and antiprincipal) solutions. We also derive some additional important results concerning the representation of T-matrices and associated normalized conjoined bases. The results in this paper are new even for completely controllable linear Hamiltonian systems. We also discuss other potential applications of our main results, in particular in the singular Sturmian theory.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA16-00611S" target="_blank" >GA16-00611S: Hamiltonovské a symplektické systémy: oscilační a spektrální teorie</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2018

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

—

Svazek periodika

264

Číslo periodika v rámci svazku

9

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

36

Strana od-do

5541-5576

Kód UT WoS článku

000426147300002

EID výsledku v databázi Scopus

2-s2.0-85040322598