Rigorous computations of homoclinic tangencies

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In this paper, we propose a rigorous computational method for detecting homoclinic tangencies and structurally unstable connecting orbits. It is a combination of several tools and algorithms, including the interval arithmetic, the subdivision algorithm, the Conley index theory, and the computational homology theory. As an example, we prove the existence of generic homoclinic tangencies in the Henon family.

Original languageEnglish (US)
Pages (from-to)280-292
Number of pages13
JournalSIAM Journal on Applied Dynamical Systems
Issue number2
StatePublished - 2006
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Modeling and Simulation


  • Computational homology
  • Conley index
  • Connecting orbit
  • Homoclinic tangency


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