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Communications in Mathematical Physics

, Volume 50, Issue 1, pp 69–77 | Cite as

A two-dimensional mapping with a strange attractor

  • M. Hénon
Article

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:xi+1=y i +1−ax i 2 ,yi+1=bx i . 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.

Keywords

Differential Equation Neural Network Manifold Statistical Physic Complex System 
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

  1. Birkhoff, G. D.: Trans. Amer. Math. Soc.18, 199 (1917)Google Scholar
  2. Engel, W.: Math. Annalen130, 11 (1955)Google Scholar
  3. Engel, W.: Math. Annalen136, 319 (1958)Google Scholar
  4. Hénon, M.: Quart. Appl. Math.27, 291 (1969)Google Scholar
  5. Lanford, O.: Work cited by Ruelle, 1975Google Scholar
  6. Lorenz, E. N.: J. atmos. Sci.20, 130 (1963)Google Scholar
  7. Pomeau, Y.: to appear (1976)Google Scholar
  8. Ruelle, D., Takens, F.: Comm. math. Phys.20, 167;23, 343 (1971)Google Scholar
  9. Ruelle, D.: Report at the Conference on “Quantum Dynamics Models and Mathematics” in Bielefeld, September 1975Google Scholar

Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • M. Hénon
    • 1
  1. 1.Observatoire de NiceNiceFrance

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