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: x i+1= y i +1- ax {/i 2}, y i+1= bx i . 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.
- Publication:
-
Communications in Mathematical Physics
- Pub Date:
- February 1976
- DOI:
- 10.1007/BF01608556
- Bibcode:
- 1976CMaPh..50...69H