Structural stability of Lorenz attractors

  • John Guckenheimer
  • R. F. Williams


Inverse Limit Tubular Neighborhood Vertical Segment Angular Sector Lorenz Attractor 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    J. Guckenheimer, A Strange, Strange Attractor, inThe Hopf Bifurcation Theorem and its Applications, ed. byJ. E. Marsden andM. McCracken, Springer-Verlag (1976), 368–381.Google Scholar
  2. [2]
    J. Guckenheimer, On Bifurcations of Maps of the Interval,Inv. Math., to appear.Google Scholar
  3. [3]
    M. Hirsch, C. Pugh, Stable Manifolds and Hyperbolic Sets,Proceedings of Symposia in Pure Mathematics XIV, Am. Math. Soc. (1970), 133–163.Google Scholar
  4. [4]
    M. Hirsch, C. Pugh, M. Shub,Invariant Manifolds, Springer Lecture Notes in Math.,583 (1977).Google Scholar
  5. [5]
    E. Lorenz, Deterministic Nonperiodic Flow,Journal of Atmospheric Sciences,20 (1963), 130–141.CrossRefGoogle Scholar
  6. [6]
    J. Palis, S. Smale, Structural Stability Theorems,Proceedings of Symposia in Pure Mathematics XIV, Am. Math. Soc., 1970, 223–231.Google Scholar
  7. [7]
    W. Parry, Symbolic dynamics and transformations of the unit interval,Trans. Amer. Math. Soc.,122 (1966), 368–378.zbMATHCrossRefMathSciNetGoogle Scholar
  8. [8]
    C. L. Siegel, J. Moser,Lectures on Celestial Mechanics, Springer-Verlag, 1971.Google Scholar
  9. [9]
    S. Smale, Differential Dynamical Systems,Bull. Am. Math. Soc.,73 (1967), 747–817.CrossRefMathSciNetGoogle Scholar
  10. [10]
    F. Takens, Partially Hyperbolic Fixed Points,Topology,10 (1971), 133–147.zbMATHCrossRefMathSciNetGoogle Scholar
  11. [11]
    R. F. Williams, Expanding Attractors,Publ. I.H.E.S., no.43 (1974), 196–203.Google Scholar
  12. [12]
    R. F. Williams,The Structure of Lorenz Attractors, Preprint.Google Scholar

Copyright information

© Publications mathématiques de l’I.H.É.S 1979

Authors and Affiliations

  • John Guckenheimer
    • 1
  • R. F. Williams
    • 2
  1. 1.University of CaliforniaSanta Cruz
  2. 2.Northwestern University and University of ColoradoUSA

Personalised recommendations