Smale Horseshoes and Homoclinic Dynamics

  • Vladimir G. Ivancevic
  • Tijana T. Ivancevic
Part of the Intelligent Systems, Control and Automation: Science and Engineering book series (ISCA, volume 32)


This Chapter is a continuation of the section 1.2.2 from Introduction. Here we give a review of current development of the Smale Horseshoe techniques of topological stretching, folding and squeezing of the phase–spaces of the chaotic systems (e.g., Duffing oscillator, see Figure 2.1), with the associated symbolic dynamics.


Periodic Orbit Homoclinic Orbit Stable Manifold Homoclinic Solution Homoclinic Point 
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Copyright information

© Springer 2007

Authors and Affiliations

  • Vladimir G. Ivancevic
    • 1
  • Tijana T. Ivancevic
    • 2
  1. 1.Defence Science and Technology OrganisationAdelaideAustralia
  2. 2.The University of AdelaideAustralia

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