Abstract
Numerical computations have shown that, for a range of values of the parameters, the Lorenz system of three non linear ordinary differential equations of first order has a strange attractor whose structure may be understood quite easily.
We show that the same properties can be observed in a simple mapping of the plane defined by: xi+1 = yi + 1 - a x 2i , yi+1 = b xi. Numerical experiments are carried out for a = 1.4, b = 0.3. Depending on the initial point (xo, yo), 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. This strange attractor has basically the same structure than a plane section of the attractor found for the Lorenz system.
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© 1976 Springer-Verlag Berlin · Heidelberg
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Henon, M., Pomeau, Y. (1976). Two strange attractors with a simple structure. In: Temam, R. (eds) Turbulence and Navier Stokes Equations. Lecture Notes in Mathematics, vol 565. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0091446
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DOI: https://doi.org/10.1007/BFb0091446
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