Physics © by Springer-Verlag 1976 A Two-dimensional Mapping with a Strange Attractor

Abstract. 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: xi+1 = yi-\-l — axj, yi+1 = bxt. Numerical experiments are carried out for a = lΛ, b = 03. Depending on the initial point (xOiyo), 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 one-dimensional manifold by a Cantor set. 1