Advertisement

Hyperbolic Periodic Orbits of Ordinary Differential Equations, Stable and Unstable Manifolds and Asymptotic Phase

  • Ken Palmer
Chapter
Part of the Mathematics and Its Applications book series (MAIA, volume 501)

Abstract

We wish to develop a theory for autonomous systems of ordinary differential equations analogous to the theory we have developed for diflfeomorphisms in Chapters 1 through 5. It turns out that the object analogous to the fixed point of a diflfeomorphism is a periodic solution rather than an equilibrium point. To some extent, we can reduce the study of a periodic solution to that of the fixed point of a diflfeomorphism by using the Poincaré map. However, first we begin by recalling a few elementary facts from the theory of ordinary differential equations.

Keywords

Ordinary Differential Equation Periodic Solution Unstable Manifold Stable Manifold Return Time 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • Ken Palmer
    • 1
  1. 1.School of Mathematical & Statistical SciencesLa Trobe UniversityBundooraAustralia

Personalised recommendations