| ŠEPITKA, Peter and Roman ŠIMON HILSCHER. Comparative index and Sturmian theory for linear Hamiltonian systems. Journal of Differential Equations. San Diego, CA USA: ACADEMIC PRESS INC ELSEVIER SCIENCE, 2017, vol. 262, No 2, p. 914-944. ISSN 0022-0396. Available from: https://dx.doi.org/10.1016/j.jde.2016.09.043. |
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@article{1355407,
author = {Šepitka, Peter and Šimon Hilscher, Roman},
article_location = {San Diego, CA USA},
article_number = {2},
doi = {http://dx.doi.org/10.1016/j.jde.2016.09.043},
keywords = {Linear Hamiltonian system; Sturmian separation theorem; Proper focal point; Comparative index; Conjoined basis; Nonoscillation; Controllability},
language = {eng},
issn = {0022-0396},
journal = {Journal of Differential Equations},
title = {Comparative index and Sturmian theory for linear Hamiltonian systems},
volume = {262},
year = {2017}
}
TY - JOUR
ID - 1355407
AU - Šepitka, Peter - Šimon Hilscher, Roman
PY - 2017
TI - Comparative index and Sturmian theory for linear Hamiltonian systems
JF - Journal of Differential Equations
VL - 262
IS - 2
SP - 914-944
EP - 914-944
PB - ACADEMIC PRESS INC ELSEVIER SCIENCE
SN - 00220396
KW - Linear Hamiltonian system
KW - Sturmian separation theorem
KW - Proper focal point
KW - Comparative index
KW - Conjoined basis
KW - Nonoscillation
KW - Controllability
N2 - The comparative index was introduced by J. Elyseeva (2007) as an efficient tool in matrix analysis, which has fundamental applications in the discrete oscillation theory. In this paper we implement the comparative index into the theory of continuous time linear Hamiltonian systems, study its properties, and apply it to obtain new Sturmian separation theorems as well as new and optimal estimates for left and right proper focal points of conjoined bases of these systems on bounded intervals. We derive our results for general possibly abnormal (or uncontrollable) linear Hamiltonian systems. The results turn out to be new even in the case of completely controllable systems. We also provide several examples, which illustrate our new theory.
ER -
ŠEPITKA, Peter and Roman ŠIMON HILSCHER. Comparative index and Sturmian theory for linear Hamiltonian systems. \textit{Journal of Differential Equations}. San Diego, CA USA: ACADEMIC PRESS INC ELSEVIER SCIENCE, 2017, vol.~262, No~2, p.~914-944. ISSN~0022-0396. Available from: https://dx.doi.org/10.1016/j.jde.2016.09.043.
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