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+1-axi2, yi+1=bxi. Numerical experiments are carried out for a=1.4, b=0.3. Depending on the initial point (x0, y0), 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. © 1976 Springer-Verlag.