The structure of Lorenz attractors

Robert F. Williams

Publications Mathématiques de l'IHÉS (1979)

  • Volume: 50, page 73-99
  • ISSN: 0073-8301

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Williams, Robert F.. "The structure of Lorenz attractors." Publications Mathématiques de l'IHÉS 50 (1979): 73-99. <http://eudml.org/doc/103966>.

@article{Williams1979,
author = {Williams, Robert F.},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {structure of Lorenz attractors; Lorenz attractor; omega-sigma-conjecture; kneading sequence; strange attractor; periodic orbits},
language = {eng},
pages = {73-99},
publisher = {Institut des Hautes Études Scientifiques},
title = {The structure of Lorenz attractors},
url = {http://eudml.org/doc/103966},
volume = {50},
year = {1979},
}

TY - JOUR
AU - Williams, Robert F.
TI - The structure of Lorenz attractors
JO - Publications Mathématiques de l'IHÉS
PY - 1979
PB - Institut des Hautes Études Scientifiques
VL - 50
SP - 73
EP - 99
LA - eng
KW - structure of Lorenz attractors; Lorenz attractor; omega-sigma-conjecture; kneading sequence; strange attractor; periodic orbits
UR - http://eudml.org/doc/103966
ER -

References

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  2. [2] EILENBERG (S.) and STEENROD (N.), Foundations of Algebraic topology, Princeton (1952), Chapter VIII. Zbl0047.41402MR14,398b
  3. [3] GUCKENHEIMER (J.), A strange, strange attractor, The Hopf Bifurcation, Marsden and McCracken, eds., Appl. Math. Sci., Springer-Verlag, 1976. 
  4. [4] GUCKENHEIMER (J.), Axiom A+no cycles ⇒ζ(t) rational, Bull. Amer. Math. Soc., 76 (1970), 592. Zbl0196.27002MR40 #8078
  5. [5] HIRSCH (M.) and PUGH (C.), The stable manifold theorem (PSPM14), op. cit., 125-163. 
  6. [6] HIRSCH (M.), PUGH (C.), SHUB (M.), Invariant manifolds, Springer Lecture Notes in Math., 583 (1977). Zbl0355.58009MR58 #18595
  7. [7] LORENZ (E. N.), Deterministic non-periodic flow, Journal of Atmospheric Sciences, 20 (1963), 130-141. 
  8. [8] MILNOR (J.) and THURSTON (W.), Iterated maps of the interval : I. The kneading matrix, preprint, I.A.S., Princeton. Zbl0664.58015
  9. [9] MILNOR (J.), THURSTON (W.), Iterated maps of the interval : II. Periodic points, preprint, I.A.S., Princeton. Zbl0664.58015
  10. [10] RÖSSLER (O. P.), An equation for continuous chaos, preprint, Universität Tübingen (to appear in Phys Letiers). 
  11. [11] RUELLE (D.) and TAKENS (F.), On the nature of turbulence, Comm. Math. Phys., 20 (1971), 167. Zbl0223.76041MR44 #1297
  12. [12] RUELLE (D.), The Lorenz Attractor and the problem of turbulence, preprint (1976), I.H.E.S. Zbl0355.76036MR57 #7690
  13. [13] SMALE (S.), Differentiable Dynamical Systems, Bull. Amer. Math. Soc., 13 (1967), 747-817. Zbl0202.55202MR37 #3598
  14. [14] SULLIVAN (D.) and WILLIAMS (R.), On the homology of attractors, preprint (1974), Topology, 15 (1976), 259-262. Zbl0332.58011MR54 #1304
  15. [15] THOM (R.), Structural stability and morphogenesis, Benjamin, Mass. (transl. D. H. FOWLER), 1975. 
  16. [16] WILLIAMS (R.), The zeta function of an attractor, Conference of the Topology of Manifolds, 1967 (ed. Hocking), Prindle, Weber and Schmidt (1968), 155-161. Zbl0179.51902MR38 #3877
  17. [17] WILLIAMS (R.), One dimensional non-wandering sets, Topology, 6 (1967), 473-487. Zbl0159.53702MR36 #897
  18. [18] WILLIAMS (R.), Expanding attractors, Publ. math. I.H.E.S., 43 (1974), 161-203. Zbl0279.58013MR50 #1289
  19. [19] GUCKENHEIMER (J.), On the bifurcation of maps of the interval, Inventiones Math., 39 (1977), 165-178. Zbl0354.58013MR55 #11312
  20. [20] THOM (R.), Mathematical Developments arising from Hilbert Problems, Proc. Symp. Pure Math., XXVII (1976) (Ed. Felix Browder), p. 59. 
  21. [21] WILLIAMS (R.), The Lorenz attractor, Turbulence Seminar, Springer Lecture Notes in Math., 615 (1977), 94-112. Zbl0363.58005MR57 #1566
  22. [22] WILLIAMS (R.), The bifurcation space of the Lorenz attractor, Procceedings of the New York Acad. of Sci. (to appear). Zbl0472.58016

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