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@inproceedings{924429, author = {Šimon Hilscher, Roman}, address = {Springfield, Missouri}, booktitle = {Proceedings of the 8th AIMS Conference on Dynamical Systems, Differential Equations and Applications}, doi = {http://dx.doi.org/10.3934/proc.2011.2011.684}, editor = {W. Feng, Z. Feng, M. Grasselli, A. Ibragimov, X. Lu, S. Siegmund, J. Voigt}, keywords = {Linear Hamiltonian system; Sturmian separation theorem; Sturmian comparison theorem; proper focal point; conjoined basis; controllability; normality}, howpublished = {paměťový nosič}, language = {eng}, location = {Springfield, Missouri}, isbn = {978-1-60133-007-9}, note = {Discrete Contin. Dynam. Systems, Suppl. 2011}, pages = {684-691}, publisher = {AIMS (American Institute of Mathematical Sciences)}, title = {On general Sturmian theory for abnormal linear Hamiltonian systems}, url = {http://aimsciences.org/journals/contentsListPro.jsp?pubID=469}, year = {2011} }
TY - JOUR ID - 924429 AU - Šimon Hilscher, Roman PY - 2011 TI - On general Sturmian theory for abnormal linear Hamiltonian systems PB - AIMS (American Institute of Mathematical Sciences) CY - Springfield, Missouri SN - 9781601330079 N1 - Discrete Contin. Dynam. Systems, Suppl. 2011 KW - Linear Hamiltonian system KW - Sturmian separation theorem KW - Sturmian comparison theorem KW - proper focal point KW - conjoined basis KW - controllability KW - normality UR - http://aimsciences.org/journals/contentsListPro.jsp?pubID=469 L2 - http://aimsciences.org/journals/contentsListPro.jsp?pubID=469 N2 - In this paper we discuss oscillation theory for linear Hamiltonian systems for which we do not impose the controllability (or equivalently normality) assumption. Based on the Sturmian separation and comparison theorems on a compact interval, derived earlier by the author for these systems, we classify them as oscillatory or nonoscillatory. Moreover, we provide comparison theorems for such oscillatory and nonoscillatory systems. One of the goals of this paper is to provide several examples illustrating this new theory. ER -
ŠIMON HILSCHER, Roman. On general Sturmian theory for abnormal linear Hamiltonian systems. In W. Feng, Z. Feng, M. Grasselli, A. Ibragimov, X. Lu, S. Siegmund, J. Voigt. \textit{Proceedings of the 8th AIMS Conference on Dynamical Systems, Differential Equations and Applications}. Springfield, Missouri: AIMS (American Institute of Mathematical Sciences). s.~684-691. ISBN~978-1-60133-007-9. doi:10.3934/proc.2011.2011.684. 2011.
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