Symplectic Dynamic Systems
This chapter continues from [86, Chapter 7] the study of symplectic dynamic systems of the form (S)
on time scales. In particular, we investigate the relationship between the nonoscillatory 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 Prüfer transformation.
$$ z^\Delta = S(t)z $$
KeywordsFocal Point Riccati Equation Dense Point Positive Definiteness Generalize Zero
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