Transversal Homoclinic Points of Diffeomorphisms and Hyperbolic Sets

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


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.


Saddle Point Unstable Manifold Implicit Function Theorem Homoclinic Orbit Exponential Dichotomy 


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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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