Genera of Conjoined Bases for (Non)oscillatory Linear
Hamiltonian Systems: Extended Theory

J 2020

Genera of Conjoined Bases for (Non)oscillatory Linear Hamiltonian Systems: Extended Theory

ŠEPITKA, Peter

Basic information

Original name

Genera of Conjoined Bases for (Non)oscillatory Linear Hamiltonian Systems: Extended Theory

Authors

ŠEPITKA, Peter (703 Slovakia, guarantor, belonging to the institution)

Edition

Journal of dynamics and differential equations. New York, Springer, 2020, 1040-7294

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10101 Pure mathematics

Country of publisher

United States of America

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

URL

Impact factor

Impact factor: 2.240

RIV identification code

RIV/00216224:14310/20:00114315

Organization unit

Faculty of Science

DOI

http://dx.doi.org/10.1007/s10884-019-09810-w

UT WoS

000541929200001

Keywords in English

Linear Hamiltonian system; Genus of conjoined bases; Riccati differential equation; Controllability; Orthogonal projector

Abstract

V originále

In this paper we study the properties of conjoined bases of a general linear Hamiltonian system without any controllability condition. When the Legendre condition holds and the system is nonoscillatory, it is known from our previous work that conjoined bases with eventually the same image form a special structure called a genus. In this work we extend the theory of genera of conjoined bases to arbitrary systems, for which the Legendre condition is not assumed and/or the system may be oscillatory. We derive a classification of all genera of conjoined bases and show that they form a complete lattice. These results are based on the relationship between subspaces of solutions of a linear control system and orthogonal projectors satisfying a certain Riccati type differential equation. The presented theory is applied in our paper (Sepitka in Discrete Contin Dyn Syst 39(4):1685-1730,2019) to general Riccati matrix differential equations for possibly uncontrollable linear Hamiltonian systems.

Links

GA16-00611S, research and development project

Name: Hamiltonovské a symplektické systémy: oscilační a spektrální teorie

Investor: Czech Science Foundation

GA19-01246S, research and development project

Name: Nová oscilační teorie pro lineární hamiltonovské a symplektické systémy

Investor: Czech Science Foundation

Citovat

ŠEPITKA, Peter. Genera of Conjoined Bases for (Non)oscillatory Linear Hamiltonian Systems: Extended Theory. Journal of dynamics and differential equations. New York: Springer, 2020, vol. 32, No 3, p. 1139-1155. ISSN 1040-7294. Available from: https://dx.doi.org/10.1007/s10884-019-09810-w.

@article{1679362,
   author = {Šepitka, Peter},
   article_location = {New York},
   article_number = {3},
   doi = {http://dx.doi.org/10.1007/s10884-019-09810-w},
   keywords = {Linear Hamiltonian system; Genus of conjoined bases; Riccati differential equation; Controllability; Orthogonal projector},
   language = {eng},
   issn = {1040-7294},
   journal = {Journal of dynamics and differential equations.},
   title = {Genera of Conjoined Bases for (Non)oscillatory Linear Hamiltonian Systems: Extended Theory},
   url = {https://doi.org/10.1007/s10884-019-09810-w},
   volume = {32},
   year = {2020}
}

TY  - JOUR
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AU  - Šepitka, Peter
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JF  - Journal of dynamics and differential equations.
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EP  - 1139-1155
PB  - Springer
SN  - 10407294
KW  - Linear Hamiltonian system
KW  - Genus of conjoined bases
KW  - Riccati differential equation
KW  - Controllability
KW  - Orthogonal projector
UR  - https://doi.org/10.1007/s10884-019-09810-w
L2  - https://doi.org/10.1007/s10884-019-09810-w
N2  - In this paper we study the properties of conjoined bases of a general linear Hamiltonian system without any controllability condition. When the Legendre condition holds and the system is nonoscillatory, it is known from our previous work that conjoined bases with eventually the same image form a special structure called a genus. In this work we extend the theory of genera of conjoined bases to arbitrary systems, for which the Legendre condition is not assumed and/or the system may be oscillatory. We derive a classification of all genera of conjoined bases and show that they form a complete lattice. These results are based on the relationship between subspaces of solutions of a linear control system and orthogonal projectors satisfying a certain Riccati type differential equation. The presented theory is applied in our paper (Sepitka in Discrete Contin Dyn Syst 39(4):1685-1730,2019) to general Riccati matrix differential equations for possibly uncontrollable linear Hamiltonian systems.
ER  -

ŠEPITKA, Peter. Genera of Conjoined Bases for (Non)oscillatory Linear Hamiltonian Systems: Extended Theory. \textit{Journal of dynamics and differential equations.}. New York: Springer, 2020, vol.~32, No~3, p.~1139-1155. ISSN~1040-7294. Available from: https://dx.doi.org/10.1007/s10884-019-09810-w.

Detailed Information on Publication Record