Strange attractors: a class of mapping of R2 which leaves some Cantor sets invariant

M. Henon defines the following mapping T:R2→R2 (1) T(x,y)=(y+1-ax2, bx) and shows by numerical experiments that if a point (x0, y0) belongs to the trapping of T, for certain values of a and b, the sequence of its iterates converges to an attractor which looks numerically like the product of a one-dimensional manifold by a Cantor set. A lot of work has been done since then about this mapping. J.H. Curry has proved in that there exists an homoclinic point belonging to the stable and unstable manifolds of one of the fixed points of T. This proof requires the use of a computer and of an approximation theorem. We define another mapping (2) T(x,y)=(y+1 - a/x, bx). The numerical study of this mapping shows that it behaves just like (1). In this case the manifolds are parts of straight lines