Structural stability of Lorenz attractors.(English)Zbl 0436.58018

MSC:

 37C70 Attractors and repellers of smooth dynamical systems and their topological structure 37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior 37C75 Stability theory for smooth dynamical systems

Zbl 0346.58007
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References:

 [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. [2] J. Guckenheimer, On Bifurcations of Maps of the Interval,Inv. Math., to appear. · Zbl 0354.58013 [3] M. Hirsch, C. Pugh, Stable Manifolds and Hyperbolic Sets,Proceedings of Symposia in Pure Mathematics XIV, Am. Math. Soc. (1970), 133–163. · Zbl 0215.53001 [4] M. Hirsch, C. Pugh, M. Shub,Invariant Manifolds, Springer Lecture Notes in Math.,583 (1977). [5] E. Lorenz, Deterministic Nonperiodic Flow,Journal of Atmospheric Sciences,20 (1963), 130–141. · Zbl 1417.37129 [6] J. Palis, S. Smale, Structural Stability Theorems,Proceedings of Symposia in Pure Mathematics XIV, Am. Math. Soc., 1970, 223–231. · Zbl 0214.50702 [7] W. Parry, Symbolic dynamics and transformations of the unit interval,Trans. Amer. Math. Soc.,122 (1966), 368–378. · Zbl 0146.18604 [8] C. L. Siegel, J. Moser,Lectures on Celestial Mechanics, Springer-Verlag, 1971. · Zbl 0312.70017 [9] S. Smale, Differential Dynamical Systems,Bull. Am. Math. Soc.,73 (1967), 747–817. · Zbl 0202.55202 [10] F. Takens, Partially Hyperbolic Fixed Points,Topology,10 (1971), 133–147. · Zbl 0214.22901 [11] R. F. Williams, Expanding Attractors,Publ. I.H.E.S., no.43 (1974), 196–203. · Zbl 0279.58013 [12] R. F. Williams,The Structure of Lorenz Attractors, Preprint. · Zbl 0484.58021
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