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Two strange attractors with a simple structure

Part of the Lecture Notes in Mathematics book series (LNM,volume 565)

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.

Keywords

  • Periodic Point
  • Strange Attractor
  • Lorenz System
  • Invariant Point
  • Limit Curve

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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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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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08060-2

  • Online ISBN: 978-3-540-37516-6

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