Informace o publikaci

Disconjugacy, transformations and quadratic functionals for symplectic dynamic systems on time scales

Logo poskytovatele
Logo poskytovatele
Autoři

DOŠLÝ Ondřej HILSCHER Roman

Rok publikování 2001
Druh Článek v odborném periodiku
Časopis / Zdroj J. Difference Equations Appl.
Fakulta / Pracoviště MU

Přírodovědecká fakulta

Citace
Obor Obecná matematika
Klíčová slova Symplectic dynamic system; time scale; quadratic functional; Roundabout theorem
Popis 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.
Související projekty:

Používáte starou verzi internetového prohlížeče. Doporučujeme aktualizovat Váš prohlížeč na nejnovější verzi.

Další info