Distribution and number of focal points for linear Hamiltonian systems

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F21%3A00118790" target="_blank" >RIV/00216224:14310/21:00118790 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1016/j.laa.2020.11.018" target="_blank" >https://doi.org/10.1016/j.laa.2020.11.018</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.laa.2020.11.018" target="_blank" >10.1016/j.laa.2020.11.018</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Distribution and number of focal points for linear Hamiltonian systems

Popis výsledku v původním jazyce

In this paper we consider the question of distribution and number of left and right focal points for conjoined bases of linear Hamiltonian differential systems. We do not assume any complete controllability (identical normality) condition. Recently we obtained the Sturmian separation theorem for this case which provides optimal lower and upper bounds for the numbers of left and right focal points of every conjoined basis in terms of the principal solutions at the endpoints of the interval. In this paper we show that for any two given integers within these bounds there exists a conjoined basis with these prescribed numbers of left and right focal points. We determine such conjoined bases by their initial conditions. Our approach is to transfer the problem through the comparative index into matrix analysis. The main results are new even for completely controllable linear Hamiltonian systems. As an application we extend a classical result for controllable systems by Reid (1971) about the existence of conjoined bases with an invertible first component.

Název v anglickém jazyce

Distribution and number of focal points for linear Hamiltonian systems

Popis výsledku anglicky

In this paper we consider the question of distribution and number of left and right focal points for conjoined bases of linear Hamiltonian differential systems. We do not assume any complete controllability (identical normality) condition. Recently we obtained the Sturmian separation theorem for this case which provides optimal lower and upper bounds for the numbers of left and right focal points of every conjoined basis in terms of the principal solutions at the endpoints of the interval. In this paper we show that for any two given integers within these bounds there exists a conjoined basis with these prescribed numbers of left and right focal points. We determine such conjoined bases by their initial conditions. Our approach is to transfer the problem through the comparative index into matrix analysis. The main results are new even for completely controllable linear Hamiltonian systems. As an application we extend a classical result for controllable systems by Reid (1971) about the existence of conjoined bases with an invertible first component.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA19-01246S" target="_blank" >GA19-01246S: Nová oscilační teorie pro lineární hamiltonovské a symplektické systémy</a><br>

Návaznosti

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

Rok uplatnění

2021

Kód důvěrnosti údajů

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

Název periodika

Linear Algebra and Its Applications

ISSN

0024-3795

e-ISSN

—

Svazek periodika

611

Číslo periodika v rámci svazku

February 2021

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

20

Strana od-do

26-45

Kód UT WoS článku

000600065400002

EID výsledku v databázi Scopus

2-s2.0-85097336569