Interval maps, factors of maps, and chaos. (English) Zbl 0448.54040


54H20 Topological dynamics (MSC2010)
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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[1] L. D. LANDAU AND E. M. LIFSCHITZ, Fluid Mechanics, Pergamon Press, Oxford, 1959. See also L. LANDAU, C. R. Acad. Sci. U. R. S. S. 44 (1944), 311-314. · Zbl 0146.22405
[2] D. RUELLE AND F. TAKENS, On the nature of turbulence, Comm. Math. Phys. 20 (1971), 167-192; 23 (1971), 343-344. · Zbl 0223.76041 · doi:10.1007/BF01646553
[3] E. LORENZ, Deterministic nonperiodic flow, J. Atmos. Sci. 20 (1963), 130-141 · Zbl 1417.37129
[4] O. E. ROSSLER, An equation for continuous chaos, Physics Letters 57A, no. 5 (19 Jul 1976), 397-398.
[5] O. E. ROSSLER, Different types of chaos in two simple differential equations, Z. Natur forsch 31a (1976), 1664-1670.
[6] J. CURRY AND J. A. YORKE, A transition from Hopf bifurcation to chaos: compute experiments with maps in R2, in Proceedings of the NSF Regional Conference in Fargo, N. D., June, 1977,
[7] R. BOWEN, A model for Couette flow data, in Springer-Verlag Lecture Notes #615 Turbulence Seminar, 1977. 8] R. M. MAY, Biological population with nonoverlapping generations: stable points, stable cycles and choas, Science 186 (1974), 645-647. · Zbl 0363.58002
[8] T. Y. Li AND J. A. YORKE, Period three implies chaos, Amer. Math. Monthly 82(1975), 985-992. JSTOR: · Zbl 0351.92021 · doi:10.2307/2318254
[9] G. PIANIGIANI, Absolutely continuous invariant measures for the process xn+=Axn(l.– xn),
[10] J. KAPLAN AND J. A. YORKE, Preturbulence: a regime observed in a fluid flow model o Lorenz, · Zbl 0443.76059 · doi:10.1007/BF01221359
[11] J. KAPLAN AND J. A. YORKE, The onset of chaos in a fluid flow model of Lorenz, Proceedings of the New York Acad. of Sciences Meeting Bifurcation, · Zbl 0445.58017
[12] J. A. YORKE AND E. D. YORKE, Metastable chaos:The transition to sustained chaoti behavior in the Lorenz model, · Zbl 0805.58007
[13] A. LASOTA AND J. A. YORKE, On the existence of invariant measures for transformation with strictly turbulent trajectories, Bull. Polish Acad. Sci. · Zbl 0357.28018
[14] A. LASOTA AND G. PIANIGIANI, Invariant measures on topological spaces, Boll. Un. Matem Ital. (5) 14B (1977), 592-603. · Zbl 0372.28019
[15] G. PIANIGIANI AND J. A. YORKE, Expanding maps on sets which are almost invariant decay and chaos, preprint. JSTOR: · Zbl 0417.28010 · doi:10.2307/1998093
[16] W. H. GOTTSCHALK AND G. A. HEDLUND, Topological Dynamics, Amer. Math. Soc. Colloq Publ. Vol. 36, 1955. · Zbl 0067.15204
[17] A. N. SHARKOVSKII, Coexistence of cycles of a continuous mapping of the line into itself, (Russian), Ukrain. Math. J. 16, no. 1 (1964), 61-71.
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