A Two-dimensional Mapping with a Strange Attractor

Lorenz (1963) has investigated a system of three first-order differential equations, whose solutions tend toward a “strange attractor”. We show that the same properties can be observed in a simple mapping of the plane defined by: .yi+,= yi+ l-a-K;, yi+l = bx,. Numerical experiments are carried out for a= 1.4, b = 0.3, Depending on the initial point (x,, yO), the sequence of points obtained by iteration of the mapping either diverges to infinity or tends to a strange attractor, which appears to be the product of a onedimensional manifold .by a Cantor set.