ŠEPITKA, Peter and Roman ŠIMON HILSCHER. Dominant and recessive solutions at infinity and genera of conjoined bases for discrete symplectic systems. Journal of Difference Equations and Applications. ABINGDON, ENGLAND: Taylor and Francis, 2017, vol. 23, No 4, p. 657-698. ISSN 1023-6198. Available from: https://dx.doi.org/10.1080/10236198.2016.1270274. |
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@article{1362613, author = {Šepitka, Peter and Šimon Hilscher, Roman}, article_location = {ABINGDON, ENGLAND}, article_number = {4}, doi = {http://dx.doi.org/10.1080/10236198.2016.1270274}, keywords = {Dominant solution at infinity; Recessive solution at infinity; Discrete symplectic system; Genus of conjoined bases; Nonoscillation; Order of abnormality; Controllability; Moore-Penrose pseudoinverse}, language = {eng}, issn = {1023-6198}, journal = {Journal of Difference Equations and Applications}, title = {Dominant and recessive solutions at infinity and genera of conjoined bases for discrete symplectic systems}, volume = {23}, year = {2017} }
TY - JOUR ID - 1362613 AU - Šepitka, Peter - Šimon Hilscher, Roman PY - 2017 TI - Dominant and recessive solutions at infinity and genera of conjoined bases for discrete symplectic systems JF - Journal of Difference Equations and Applications VL - 23 IS - 4 SP - 657-698 EP - 657-698 PB - Taylor and Francis SN - 10236198 KW - Dominant solution at infinity KW - Recessive solution at infinity KW - Discrete symplectic system KW - Genus of conjoined bases KW - Nonoscillation KW - Order of abnormality KW - Controllability KW - Moore-Penrose pseudoinverse N2 - In this paper we introduce the theory of dominant solutions at infinity for nonoscillatory discrete symplectic systems without any controllability assumption. Such solutions represent an opposite concept to recessive solutions at infinity, which were recently developed for such systems by the authors. Our main results include: (i) the existence of dominant solutions at infinity for all ranks in a given range depending on the order of abnormality of the system, (ii) construction of dominant solutions at infinity with eventually the same image, (iii) classification of dominant and recessive solutions at infinity with eventually the same image, (iv) limit characterization of recessive solutions at infinity in terms of dominant solutions at infinity and vice versa, and (v) Reid's construction of the minimal recessive solution at infinity. These results are based on a new theory of genera of conjoined bases for symplectic systems developed for this purpose in this paper. ER -
ŠEPITKA, Peter and Roman ŠIMON HILSCHER. Dominant and recessive solutions at infinity and genera of conjoined bases for discrete symplectic systems. \textit{Journal of Difference Equations and Applications}. ABINGDON, ENGLAND: Taylor and Francis, 2017, vol.~23, No~4, p.~657-698. ISSN~1023-6198. Available from: https://dx.doi.org/10.1080/10236198.2016.1270274.
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