Communications in Mathematical Physics

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

A two-dimensional mapping with a strange attractor

  • M. Hénon


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.


Differential Equation Neural Network Manifold Statistical Physic Complex System 
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Copyright information

© Springer-Verlag 1976

Authors and Affiliations

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

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