Advertisement

Communications in Mathematical Physics

, Volume 68, Issue 2, pp 129–140 | Cite as

On the Hénon transformation

  • James H. Curry
Article

Abstract

In [4] Hénon studied a transformation which maps the plane into itself and appears to have an attractor with locally the structure of a Cantor set cross an interval. By making use of the characteristic exponent, frequency spectrum, and a theorem of Smale, our numerical experiments provide evidence for the existence of two distinct strange attractors for some parameter values, an exponential rate of mixing for the parameter values studied by Hénon, and an argument that there is a Cantor set in the trapping region of Hénon.

Keywords

Neural Network Statistical Physic Complex System Numerical Experiment Nonlinear Dynamics 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bowen, R.: A model of Couette flow data. Turbulence Seminar Berkeley, p. 128. In: Lecture notes in mathematics, Vol. 615. Berlin, Heidelberg, New York: Springer 1977Google Scholar
  2. 2.
    Feit, S.D.: Characteristic exponents and strange attractors. Preprint (1977)Google Scholar
  3. 3.
    Gollub, J.P., Swinney, H.L.: Onset of turbulence in a rotating fluid. Phys. Rev. Lett.35, 927 (1975)Google Scholar
  4. 4.
    Hénon, M.: A two-dimensional mapping with a strange attractor. Commun. Math. Phys.50, 69 (1976)Google Scholar
  5. 5.
    Newhouse, S.E.: The abundance of wild hyperbolic sets and non-smooth stable sets of diffeomorphisms. Preprint (1977)Google Scholar
  6. 6.
    Ruelle, D.: Dynamical systems with turbulent behavior. International Mathematical Physics Conference in Rome (1977)Google Scholar
  7. 7.
    Smale, S.: Differentiable dynamical systems. Bull. AMS73, 747 (1967)Google Scholar

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • James H. Curry
    • 1
    • 2
  1. 1.Advanced Study ProgramNational Center for Atmospheric ResearchBoulder
  2. 2.Department of MeteorologyMassachusetts Institute of TechnologyCambridgeUSA

Personalised recommendations