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: x i + 1 = y i + 1 − a x i 2 , y i + 1 = b x i https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203734636/af41cd04-f159-4387-917e-fec41ddcf0d6/content/inequ33_341_1.tif"/> . Numerical experiments are carried out for a =1.4, b = 0.3. Depending on the initial point (x 0, y 0), 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.
