Tohoku Mathematical Journal

Interval maps, factors of maps, and chaos

Joseph Auslander and James A. Yorke

Full-text: Open access

Article information

Source
Tohoku Math. J. (2) Volume 32, Number 2 (1980), 177-188.

Dates
First available in Project Euclid: 3 May 2007

Permanent link to this document
http://projecteuclid.org/euclid.tmj/1178229634

Digital Object Identifier
doi:10.2748/tmj/1178229634

Mathematical Reviews number (MathSciNet)
MR0580273

Zentralblatt MATH identifier
0448.54040

Subjects
Primary: 58F12
Secondary: 58F13

Citation

Auslander, Joseph; Yorke, James A. Interval maps, factors of maps, and chaos. Tohoku Math. J. (2) 32 (1980), no. 2, 177--188. doi:10.2748/tmj/1178229634. http://projecteuclid.org/euclid.tmj/1178229634.


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References

  • [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.
  • [2] D. RUELLE AND F. TAKENS, On the nature of turbulence, Comm. Math. Phys. 20 (1971), 167-192; 23 (1971), 343-344.
  • [3] E. LORENZ, Deterministic nonperiodic flow, J. Atmos. Sci. 20 (1963), 130-141
  • [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, to appear.
  • [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.
  • [9] T. Y. Li AND J. A. YORKE, Period three implies chaos, Amer. Math. Monthly 82(1975), 985-992.
  • [10] G. PIANIGIANI, Absolutely continuous invariant measures for the process xn+=Axn(l.-- xn), preprint.
  • [11] J. KAPLAN AND J. A. YORKE, Preturbulence: a regime observed in a fluid flow model o Lorenz, preprint.
  • [12] 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, to appear.
  • [13] J. A. YORKE AND E. D. YORKE, Metastable chaos:The transition to sustained chaoti behavior in the Lorenz model, preprint.
  • [14] A. LASOTA AND J. A. YORKE, On the existence of invariant measures for transformation with strictly turbulent trajectories, Bull. Polish Acad. Sci.
  • [15] A. LASOTA AND G. PIANIGIANI, Invariant measures on topological spaces, Boll. Un. Matem Ital. (5) 14B (1977), 592-603.
  • [16] G. PIANIGIANI AND J. A. YORKE, Expanding maps on sets which are almost invariant decay and chaos, preprint.
  • [17] W. H. GOTTSCHALK AND G. A. HEDLUND, Topological Dynamics, Amer. Math. Soc. Colloq Publ. Vol. 36, 1955.
  • [18] 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.