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@article{1400916, author = {Šepitka, Peter and Šimon Hilscher, Roman}, article_location = {Amsterdam}, article_number = {9}, doi = {http://dx.doi.org/10.1016/j.jde.2018.01.016}, keywords = {Linear Hamiltonian system; Proper focal point; Principal solution; Antiprincipal solution; Controllability}, language = {eng}, issn = {0022-0396}, journal = {Journal of Differential Equations}, title = {Focal points and principal solutions of linear Hamiltonian systems revisited}, url = {http://dx.doi.org/10.1016/j.jde.2018.01.016}, volume = {264}, year = {2018} }
TY - JOUR ID - 1400916 AU - Šepitka, Peter - Šimon Hilscher, Roman PY - 2018 TI - Focal points and principal solutions of linear Hamiltonian systems revisited JF - Journal of Differential Equations VL - 264 IS - 9 SP - 5541-5576 EP - 5541-5576 PB - Elsevier SN - 00220396 KW - Linear Hamiltonian system KW - Proper focal point KW - Principal solution KW - Antiprincipal solution KW - Controllability UR - http://dx.doi.org/10.1016/j.jde.2018.01.016 N2 - 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. ER -
ŠEPITKA, Peter a Roman ŠIMON HILSCHER. Focal points and principal solutions of linear Hamiltonian systems revisited. \textit{Journal of Differential Equations}. Amsterdam: Elsevier, 2018, roč.~264, č.~9, s.~5541-5576. ISSN~0022-0396. Dostupné z: https://dx.doi.org/10.1016/j.jde.2018.01.016.
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