Springer Online Journal Archives 1860-2000
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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