Structural stability of Lorenz attractors
John Guckenheimer; Robert F. Williams
Publications Mathématiques de l'IHÉS (1979)
- Volume: 50, page 59-72
- ISSN: 0073-8301
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topGuckenheimer, John, and Williams, Robert F.. "Structural stability of Lorenz attractors." Publications Mathématiques de l'IHÉS 50 (1979): 59-72. <http://eudml.org/doc/103965>.
@article{Guckenheimer1979,
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 = {http://eudml.org/doc/103965},
volume = {50},
year = {1979},
}
TY - JOUR
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 - http://eudml.org/doc/103965
ER -
References
top- [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] J. GUCKENHEIMER, On Bifurcations of Maps of the Interval, Inv. Math., to appear. Zbl0354.58013
- [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] M. HIRSCH, C. PUGH, M. SHUB, Invariant Manifolds, Springer Lecture Notes in Math., 583 (1977). Zbl0355.58009MR58 #18595
- [5] E. LORENZ, Deterministic Nonperiodic Flow, Journal of Atmospheric Sciences, 20 (1963), 130-141.
- [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] W. PARRY, Symbolic dynamics and transformations of the unit interval, Trans. Amer. Math. Soc., 122 (1966), 368-378. Zbl0146.18604MR33 #5846
- [8] C. L. SIEGEL, J. MOSER, Lectures on Celestial Mechanics, Springer-Verlag, 1971. Zbl0312.70017MR58 #19464
- [9] S. SMALE, Differential Dynamical Systems, Bull. Am. Math. Soc., 73 (1967), 747-817. Zbl0202.55202MR37 #3598
- [10] F. TAKENS, Partially Hyperbolic Fixed Points, Topology, 10 (1971), 133-147. Zbl0214.22901MR46 #6399
- [11] R. F. WILLIAMS, Expanding Attractors, Publ. I.H.E.S., no. 43 (1974), 196-203. Zbl0279.58013MR50 #1289
- [12] R. F. WILLIAMS, The Structure of Lorenz Attractors, Preprint. Zbl0484.58021
Citations in EuDML Documents
top- Rafael Labarca, Carlos Gustavo Moreira, Essential dynamics for Lorenz maps on the real line and the lexicographical world
- C. A. Morales, Lorenz attractor through saddle-node bifurcations
- C. A Morales, Poincaré-Hopf index and partial hyperbolicity
- Rodrigo Bamon, Rafael Labarca, Ricardo Mañé, Maria-José Pacífico, The explosion of singular cycles
- Stephano Luzzatto, Warwick Tucker, Non-uniformly expanding dynamics in maps with singularities and criticalities
- Roger J. Metzger, Sinai-Ruelle-Bowen measures for contracting Lorenz maps and flows
- Aubin Arroyo, Federico Rodriguez Hertz, Homoclinic bifurcations and uniform hyperbolicity for three-dimensional flows
- Lluis Alsedà, Antonio Falcó, On the topological dynamics and phase-locking renormalization of Lorenz-like maps
- C. A. Morales, E. R. Pujals, Singular strange attractors on the boundary of Morse-Smale systems
- J. Palis, A global perspective for non-conservative dynamics
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