, Volume 50, Issue 1, pp 69-77

A two-dimensional mapping with a strange attractor

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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−ax i 2 ,y i+1=bx i . Numerical experiments are carried out fora=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.