A two-dimensional mapping with a strange attractor
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- Hénon, M. Commun.Math. Phys. (1976) 50: 69. doi:10.1007/BF01608556
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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 fora=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.