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: \({x_{i + 1}} = {y_i} + 1 - ax_i^2,{y_{i + 1}} = b{x_i}\). 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 onedimensional manifold.by a Cantor set.
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© 1976 Springer Science+Business Media New York
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Hénon, M. (1976). A Two-dimensional Mapping with a Strange Attractor. In: Hunt, B.R., Li, TY., Kennedy, J.A., Nusse, H.E. (eds) The Theory of Chaotic Attractors. Springer, New York, NY. https://doi.org/10.1007/978-0-387-21830-4_8
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DOI: https://doi.org/10.1007/978-0-387-21830-4_8
Publisher Name: Springer, New York, NY
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