On the Hénon transformation

In 4] Hénon studied a transformation which maps the plane into itself and appears to have an attractor with locally the structure of a Cantor set cross an interval. By making use of the characteristic exponent, frequency spectrum, and a theorem of Smale, our numerical experiments provide evidence for the existence of two distinct strange attractors for some parameter values, an exponential rate of mixing for the parameter values studied by Hénon, and an argument that there is a Cantor set in the trapping region of Hénon.On leave from the Department of Mathematics, University of Colorado, Boulder, Colorado 80309, USAThe National Center for Atmospheric Research is sponsored by the National Science Foundation