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Symplectic Dynamic Systems

In: Advances in Dynamic Equations on Time Scales

Author

Listed:
  • Ondřej Došlý

    (Masaryk University, Department of Mathematics)

  • Stefan Hilger

    (Katholische Universität Eichstätt, Didaktik der Physik)

  • Roman Hilscher

    (Michigan State University, Department of Mathematics)

Abstract

This chapter continues from [86, Chapter 7] the study of symplectic dynamic systems of the form (S) $$ z^\Delta = S(t)z $$ 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.

Suggested Citation

  • Ondřej Došlý & Stefan Hilger & Roman Hilscher, 2003. "Symplectic Dynamic Systems," Springer Books, in: Martin Bohner & Allan Peterson (ed.), Advances in Dynamic Equations on Time Scales, chapter 0, pages 293-334, Springer.
    • Handle: RePEc:spr:sprchp:978-0-8176-8230-9_10
    DOI: 10.1007/978-0-8176-8230-9_10
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