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Communications in Mathematical Physics

, Volume 67, Issue 2, pp 137–146 | Cite as

Shift automorphisms in the Hénon mapping

  • R. Devaney
  • Z. Nitecki
Article

Abstract

We investigate the global behavior of the quadratic diffeomorphism of the plane given byH(x,y)=(1+yAx2,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.

Keywords

Neural Network Statistical Physic Complex System Nonlinear Dynamics Quantum Computing 
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Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • R. Devaney
    • 1
  • Z. Nitecki
    • 1
  1. 1.Department of MathematicsTufts UniversityMedfordUSA

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