Symplectic Dynamic Systems

Ondřej Došlý (), Stefan Hilger () and Roman Hilscher ()
Additional contact information
Ondřej Došlý: Masaryk University, Department of Mathematics
Stefan Hilger: Katholische Universität Eichstätt, Didaktik der Physik
Roman Hilscher: Michigan State University, Department of Mathematics

Chapter Chapter 10 in Advances in Dynamic Equations on Time Scales, 2003, pp 293-334 from Springer

Abstract: 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.

Keywords: Focal Point; Riccati Equation; Dense Point; Positive Definiteness; Generalize Zero (search for similar items in EconPapers)
Date: 2003
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-8176-8230-9_10

Ordering information: This item can be ordered from
http://www.springer.com/9780817682309

DOI: 10.1007/978-0-8176-8230-9_10

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().