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Guckenheimer, John; Williams, R. F.

Structural stability of Lorenz attractors. (English) Zbl 0436.58018

Publ. Math., Inst. Hautes Étud. Sci. 50, 59-72 (1979).
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scan of Zbl 0436.58018

Cited in 7 Reviews
Cited in 248 Documents

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

Keywords:

kneading sequence; the geometric Lorenz attractor is structurally stable of codimension 2

Citations:

Zbl 0346.58007
PDFBibTeX XMLCite
\textit{J. Guckenheimer} and \textit{R. F. Williams}, Publ. Math., Inst. Hautes Étud. Sci. 50, 59--72 (1979; Zbl 0436.58018)
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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 · doi:10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2
[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 · doi:10.1090/S0002-9947-1966-0197683-5
[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 · doi:10.1090/S0002-9904-1967-11798-1
[10] F. Takens, Partially Hyperbolic Fixed Points,Topology,10 (1971), 133–147. · Zbl 0214.22901 · doi:10.1016/0040-9383(71)90035-8
[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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