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References
L.D. Landau and E.M. Lifshitz, Fluid Mechanics, Pergamon Press, Oxford, 1959 (see pp. 105–107).
L.D. Landau, C.R. Acad. Sci., U.R.S.S. 44(1944), 311.
D. Ruelle and F. Takens, On the nature of turbulence, Comm. Math. Phys. 20(1971), 167–192; 23(1971), 343–344.
R. Bowen, A model for Couette flow data, in Springer Verlag Lecture Notes #615: Turbulence Seminar, 1977.
E.N. Lorenz, Deterministic nonperiodic flows, J. Atmos. Sci. 20(1963), 130–141.
J. Curry, A generalized Lorenz system, preprint.
M.G. Julia, Mémoire sur l'itération des fonctions rationnelles, J. Math. Pures et Appl., Serie 7 tome 4(1918), 47–245.
J.L. Kaplan and J.A. Yorke, Preturbulence: a regime observed in a fluid flow model of Lorenz, a preprint.
J.L. Kaplan and J.A. Yorke, The onset of chaos in a fluid flow model of Lorenz, in Proceedings of the New York Acad. of Sci. meeting on Bifurcation, held in November 1977 in New York City.
J.A. Yorke and E.D. Yorke, Metastable chaos: the transition to sustained chaotic oscillations in a model of Lorenz, a preprint.
K.A. Robbins, A new approach to subcritical instability and Turbulent transitions in a simple dynamo, Math. Proc. Cambridge Phil. Soc., to appear.
O.E. Rossler, Horseshoe-map chaos in the Lorenz equation, Physics Letters 60A(1977), to appear.
Efraimovich, Bikov, and Silnikov, The origin and structure of the Lorenz attractor, Dokl. Acad. Nauk SSR 234(1977), 336–339.
M. Lucke, Statistical dynamics of the Lorenz model, J. Statistical Physics 15(1976), 455–474.
J. Guckenheimer and R.F. Williams, to appear.
J.B. McLaughlin and P.C. Martin, Transition to turbulence in a statically stressed fluid system, Phys. Rev. A12(1975), 186–203.
O.E. Lanford, Qualitative and statistical theory of dissipative systems (preprint).
J.C. Oxtoby and S.M. Ulam, Measure preserving homeomorphisms and metrical transitivity, Ann. Math. 42(1941), 87–92.
J. Moser, A rapidly convergent iteration method, Part II, Ann. Scuola Norm. Sup. Pisa 20(1965), 499–535.
K. Sitnikov, Existence of oscillating motions for the three-body problem, Dokl. Akad. Nauk 133(1960), 303–306.
V.A. Plis, On recurrent motions in periodic systems of two differential equations, Differentsial'nye Uravneniya 3(1967), 722–732.
V.A. Plis, Some problems in the behavior of solutions of periodic dissipative second-order systems, ibid, 2(1966).
F. Rannou, Numerical study of discrete plane area-preserving mappings, Astron. and Astrophys. 31(1974), 289–301.
H. Hénon, A two-dimensional mapping with a strange attraction, Comm. Math. Phys. 50(1976), 69–77.
J.R. Beddington, C.A. Free, and J.H. Lauton, Dynamic complexity in predator-prey models framed in difference equations, Nature 255(1975), 58–60.
P. Stein and S. Ulam, Nonlinear transformation studies on electronic computers, Rozprawy Metamat. 39(1964), 401–484.
D. Aronson and R. McGehee, in this volume.
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Curry, J.H., Yorke, J.A. (1978). A transition from hopf bifurcation to chaos: Computer experiments with maps on R2 . In: Markley, N.G., Martin, J.C., Perrizo, W. (eds) The Structure of Attractors in Dynamical Systems. Lecture Notes in Mathematics, vol 668. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0101779
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DOI: https://doi.org/10.1007/BFb0101779
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