O.Dosly, S.Hilger, R.Hilscher
Symplectic dynamic systems
Abstract
This chapter continues from [1, Chapter 7] the study of symplectic dynamic systems
of the form (S)
on time scales. In particular, we investigate the relationship between the oscillatory
properties (no focal points) of certain conjoined bases of (S), the solvability of the
corresponding Riccati matrix dynamic equation, and the positivity of the associated quadratic
functional. Furthermore, we establish Sturmian separation and comparison theorems. As
applications of the transformation theory of symplectic dynamic systems, we study trigonometric
and hyperbolic symplectic systems, and the Pruefer transformation.
[1] M.Bohner, A.Peterson, Dynamic Equations on Time Scales. An Introduction with Applications.
Birkhauser, Boston, 2001.