Symplectic Dynamic Systems

  • Ondřej Došlý
  • Stefan Hilger
  • Roman Hilscher


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.


Focal Point Riccati Equation Dense Point Positive Definiteness Generalize Zero 
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Copyright information

© Springer Science+Business Media New York 2003

Authors and Affiliations

  • Ondřej Došlý
    • 1
  • Stefan Hilger
    • 2
  • Roman Hilscher
    • 3
  1. 1.Department of MathematicsMasaryk UniversityBrnoCzech Republic
  2. 2.Didaktik der PhysikKatholische Universität EichstättEichstättGermany
  3. 3.Department of MathematicsMichigan State UniversityEast LansingUSA

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