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@article{488382,
author = {Hilscher, Roman},
article_location = {New York},
article_number = {2},
keywords = {time scale; symplectic system; linear Hamiltonian system; quadratic functional; disconjugacy; focal point; principal solution; Riccati equation; Jacobi condition; Legendre condition},
language = {eng},
issn = {0095-4616},
journal = {Applied Mathematics and Optimization},
title = {Reid roundabout theorem for symplectic dynamic systems on time scales},
volume = {43},
year = {2001}
}
TY - JOUR
ID - 488382
AU - Hilscher, Roman
PY - 2001
TI - Reid roundabout theorem for symplectic dynamic systems on time scales
JF - Applied Mathematics and Optimization
VL - 43
IS - 2
SP - 129-146
EP - 129-146
PB - Springer-Verlag
SN - 00954616
KW - time scale
KW - symplectic system
KW - linear Hamiltonian system
KW - quadratic functional
KW - disconjugacy
KW - focal point
KW - principal solution
KW - Riccati equation
KW - Jacobi condition
KW - Legendre condition
N2 - The principal aim of this paper is to state and prove the so called Reid roundabout theorem for symplectic dynamic system (S) z\Delta=Stz on an arbitrary time scale T, so that the well known case of differential linear Hamiltonian systems (T=R) and recently developed case of discrete symplectic systems (T=Z) are unified. We list conditions which are equivalent to the positivity of the quadratic functional associated with (S), e.g. disconjugacy (in terms of no focal points of a conjoined basis) of (S), no generalized zeros for vector solutions of (S), the existence of a solution to the corresponding Riccati matrix equation. A certain normality assumption is employed. The result requires treatment of the quadratic functionals both with general and separated boundary conditions.
ER -
HILSCHER, Roman. Reid roundabout theorem for symplectic dynamic systems on time scales. \textit{Applied Mathematics and Optimization}. New York: Springer-Verlag, 2001, vol.~43, No~2, p.~129-146. ISSN~0095-4616.
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