| DOŠLÝ, Ondřej and Roman HILSCHER. Disconjugacy, transformations and quadratic functionals for symplectic dynamic systems on time scales (Disconjugacy,transformations and quadratic functionals for symplectic dynamic systems on time scales). J. Difference Equations Appl. San Diego, 2001, vol. 7, No 3, p. 265-294. ISSN 1023-6198. |
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@article{366592,
author = {Došlý, Ondřej and Hilscher, Roman},
article_location = {San Diego},
article_number = {3},
keywords = {Symplectic dynamic system; time scale; quadratic functional; Roundabout theorem},
language = {eng},
issn = {1023-6198},
journal = {J. Difference Equations Appl.},
title = {Disconjugacy, transformations and quadratic functionals for symplectic dynamic systems on time scales},
volume = {7},
year = {2001}
}
TY - JOUR
ID - 366592
AU - Došlý, Ondřej - Hilscher, Roman
PY - 2001
TI - Disconjugacy, transformations and quadratic functionals for symplectic dynamic systems on time scales
JF - J. Difference Equations Appl.
VL - 7
IS - 3
SP - 265
EP - 265
SN - 10236198
KW - Symplectic dynamic system
KW - time scale
KW - quadratic functional
KW - Roundabout theorem
N2 - In this paper we study qualitative properties of the so-called symplectic dynamic system (S) z^\Delta=S(t)z on an arbitrary time scale T, providing a unified theory for discrete symplectic systems (T=Z) and differential linear Hamiltonian systems (T=R). We define disconjugacy (no focal points) for conjoined bases of (S) and prove, under a certain minimal normality assumption, that disconjugacy of (S) on the interval under consideration is equivalent to the positivity of the associated quadratic functional. Such statement is commonly called Jacobi condition. We discuss also solvability of the corresponding Riccati matrix equation and transformations. This work may be regarded as a generalization of the results recently obtained by the second author for linear Hamiltonian systems on time scales.
ER -
DOŠLÝ, Ondřej and Roman HILSCHER. Disconjugacy, transformations and quadratic functionals for symplectic dynamic systems on time scales (Disconjugacy,transformations and quadratic functionals for symplectic dynamic systems on time scales). \textit{J. Difference Equations Appl.}. San Diego, 2001, vol.~7, No~3, p.~265-294. ISSN~1023-6198.
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