Transversal Homoclinic Points of Diffeomorphisms and Hyperbolic Sets

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

Abstract

Up till now our only examples of hyperbolic sets have been hyperbolic fixed points and periodic orbits. In this chapter we give an example of a hyperbolic set which is infinite. Moreover, even though the set consists of only two distinct orbits, we shall show in Chapter 5 that in its neighbourhood the diffeomorphism has chaotic dynamics.

Keywords

Saddle Point Unstable Manifold Implicit Function Theorem Homoclinic Orbit Exponential Dichotomy 
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.

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Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

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

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