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Shift automorphisms in the Hénon mapping

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Abstract

We investigate the global behavior of the quadratic diffeomorphism of the plane given byH(x,y)=(1+y−Ax 2,Bx). Numerical work by Hénon, Curry, and Feit indicate that, for certain values of the parameters, this mapping admits a “strange attractor”. Here we show that, forA small enough, all points in the plane eventually move to infinity under iteration ofH. On the other hand, whenA is large enough, the nonwandering set ofH is topologically conjugate to the shift automorphism on two symbols.

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Authors and Affiliations

  1. Department of Mathematics, Tufts University, 02155, Medford, Massachusetts, USA

    R. Devaney & Z. Nitecki

Authors
  1. R. Devaney
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  2. Z. Nitecki
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Additional information

Communicated by J. L. Lebowitz

Partially supported by NSF Grant MCS 77-00430

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Devaney, R., Nitecki, Z. Shift automorphisms in the Hénon mapping. Commun.Math. Phys. 67, 137–146 (1979). https://doi.org/10.1007/BF01221362

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  • DOI: https://doi.org/10.1007/BF01221362

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