Rigorous Computations of Homoclinic Tangencies

@article{Arai2006RigorousCO,
  title={Rigorous Computations of Homoclinic Tangencies},
  author={Zin Arai and Konstantin Mischaikow},
  journal={SIAM J. Applied Dynamical Systems},
  year={2006},
  volume={5},
  pages={280-292}
}
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 Hénon family. 
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