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Existence of a homoclinic point for the Hénon map

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Abstract

We prove analytically that for the Hénon map of the plane into itself (s, t)↦(t+1−1.4a 2, 0.3s), there exists a transversal homoclinic point.

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References

  1. Curry, J.H.: On the Hénon transformation. Commun. Math. Phys.68, 129–140 (1979)

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  2. Hénon, M.: A two-dimensional mapping with a strange attractor. Commun. Math. Phys.50, 69–77 (1976)

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  3. Marotto, F.R.: Chaotic behavior in the Hénon mapping. Commun. Math. Phys.68, 187–194 (1979)

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Authors and Affiliations

  1. Institute of Mathematics, Warsaw University, PL-00-901, Warsaw

    Michał Misiurewicz

  2. Institute of Applied Mathematics and Statistics, SGGW-Agricultural University, PL-02-975, Warsaw, Poland

    Bolesław Szewc

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  1. Michał Misiurewicz
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  2. Bolesław Szewc
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Communicated by D. Ruelle

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Misiurewicz, M., Szewc, B. Existence of a homoclinic point for the Hénon map. Commun.Math. Phys. 75, 285–291 (1980). https://doi.org/10.1007/BF01212713

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  • DOI: https://doi.org/10.1007/BF01212713

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