Shift Automorphisms in the Hénon Mapping

We investigate the global behavior of the quadratic diffeomorphism of the plane given by H(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, for A small enough, all points in the plane eventually move to infinity under iteration of H. On the other hand, when A is large enough, the nonwandering set of H is topologically conjugate to the shift automorphism on two symbols.