Reid Roundabout Theorem for Symplectic Dynamic Systems on Time Scales

Reid Roundabout Theorem for Symplectic Dynamic Systems on Time Scales The principal aim of this paper is to state and prove the so-called Reid roundabout theorem for the symplectic dynamic system (S) z Δ = \cal S t z on an arbitrary time scale \Bbb T , so that the well known case of differential linear Hamiltonian systems ( \Bbb T = \Bbb R ) and the recently developed case of discrete symplectic systems ( \Bbb T = \Bbb Z ) are unified. We list conditions which are equivalent to the positivity of the quadratic functional associated with (S), e.g. disconjugacy (in terms of no focal points of a conjoined basis) of (S), no generalized zeros for vector solutions of (S), and the existence of a solution to the corresponding Riccati matrix equation. A certain normality assumption is employed. The result requires treatment of the quadratic functionals both with general and separated boundary conditions. Applied Mathematics and Optimization Springer Journals

Reid Roundabout Theorem for Symplectic Dynamic Systems on Time Scales

Loading next page...
Copyright © Inc. by 2000 Springer-Verlag New York
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
Publisher site
See Article on Publisher Site

There are no references for this article.

You’re reading a free preview. Subscribe to read the entire article.

DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

It’s easy to organize your research with our built-in tools.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

Monthly Plan

  • Read unlimited articles
  • Personalized recommendations
  • No expiration
  • Print 20 pages per month
  • 20% off on PDF purchases
  • Organize your research
  • Get updates on your journals and topic searches


Start Free Trial

14-day Free Trial

Best Deal — 39% off

Annual Plan

  • All the features of the Professional Plan, but for 39% off!
  • Billed annually
  • No expiration
  • For the normal price of 10 articles elsewhere, you get one full year of unlimited access to articles.



billed annually
Start Free Trial

14-day Free Trial