Structural stability of Lorenz attractors

John Guckenheimer; Robert F. Williams

Publications Mathématiques de l'IHÉS (1979)

  • Volume: 50, page 59-72
  • ISSN: 0073-8301

How to cite


Guckenheimer, John, and Williams, Robert F.. "Structural stability of Lorenz attractors." Publications Mathématiques de l'IHÉS 50 (1979): 59-72. <>.

author = {Guckenheimer, John, Williams, Robert F.},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {kneading sequence; the geometric Lorenz attractor is structurally stable of codimension 2},
language = {eng},
pages = {59-72},
publisher = {Institut des Hautes Études Scientifiques},
title = {Structural stability of Lorenz attractors},
url = {},
volume = {50},
year = {1979},

AU - Guckenheimer, John
AU - Williams, Robert F.
TI - Structural stability of Lorenz attractors
JO - Publications Mathématiques de l'IHÉS
PY - 1979
PB - Institut des Hautes Études Scientifiques
VL - 50
SP - 59
EP - 72
LA - eng
KW - kneading sequence; the geometric Lorenz attractor is structurally stable of codimension 2
UR -
ER -


  1. [1] J. GUCKENHEIMER, A Strange, Strange Attractor, in The Hopf Bifurcation Theorem and its Applications, ed. by J. E. MARSDEN and M. MCCRACKEN, Springer-Verlag (1976), 368-381. 
  2. [2] J. GUCKENHEIMER, On Bifurcations of Maps of the Interval, Inv. Math., to appear. Zbl0354.58013
  3. [3] M. HIRSCH, C. PUGH, Stable Manifolds and Hyperbolic Sets, Proceedings of Symposia in Pure Mathematics XIV, Am. Math. Soc. (1970), 133-163. Zbl0215.53001MR42 #6872
  4. [4] M. HIRSCH, C. PUGH, M. SHUB, Invariant Manifolds, Springer Lecture Notes in Math., 583 (1977). Zbl0355.58009MR58 #18595
  5. [5] E. LORENZ, Deterministic Nonperiodic Flow, Journal of Atmospheric Sciences, 20 (1963), 130-141. 
  6. [6] J. PALIS, S. SMALE, Structural Stability Theorems, Proceedings of Symposia in Pure Mathematics XIV, Am. Math. Soc., 1970, 223-231. Zbl0214.50702MR42 #2505
  7. [7] W. PARRY, Symbolic dynamics and transformations of the unit interval, Trans. Amer. Math. Soc., 122 (1966), 368-378. Zbl0146.18604MR33 #5846
  8. [8] C. L. SIEGEL, J. MOSER, Lectures on Celestial Mechanics, Springer-Verlag, 1971. Zbl0312.70017MR58 #19464
  9. [9] S. SMALE, Differential Dynamical Systems, Bull. Am. Math. Soc., 73 (1967), 747-817. Zbl0202.55202MR37 #3598
  10. [10] F. TAKENS, Partially Hyperbolic Fixed Points, Topology, 10 (1971), 133-147. Zbl0214.22901MR46 #6399
  11. [11] R. F. WILLIAMS, Expanding Attractors, Publ. I.H.E.S., no. 43 (1974), 196-203. Zbl0279.58013MR50 #1289
  12. [12] R. F. WILLIAMS, The Structure of Lorenz Attractors, Preprint. Zbl0484.58021

Citations in EuDML Documents

  1. C. A Morales, Poincaré-Hopf index and partial hyperbolicity
  2. Rafael Labarca, Carlos Gustavo Moreira, Essential dynamics for Lorenz maps on the real line and the lexicographical world
  3. C. A. Morales, Lorenz attractor through saddle-node bifurcations
  4. Rodrigo Bamon, Rafael Labarca, Ricardo Mañé, Maria-José Pacífico, The explosion of singular cycles
  5. Stephano Luzzatto, Warwick Tucker, Non-uniformly expanding dynamics in maps with singularities and criticalities
  6. Roger J. Metzger, Sinai-Ruelle-Bowen measures for contracting Lorenz maps and flows
  7. Aubin Arroyo, Federico Rodriguez Hertz, Homoclinic bifurcations and uniform hyperbolicity for three-dimensional flows
  8. Lluis Alsedà, Antonio Falcó, On the topological dynamics and phase-locking renormalization of Lorenz-like maps
  9. C. A. Morales, E. R. Pujals, Singular strange attractors on the boundary of Morse-Smale systems
  10. J. Palis, A global perspective for non-conservative dynamics

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