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Preturbulence: A regime observed in a fluid flow model of Lorenz. (English) Zbl 0443.76059
[1]Kaplan, J.L., Yorke, J.A.: The onset of chaos in a fluid flow model of Lorenz. Proc. NY Acad. Sci. (to appear)
[2]Lorenz, E.N.: Deterministic nonperiodic flow. J. Atmos. Sci.20, 130-141 (1963) · doi:10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2
[3]Guckenheimer, J.: A strange attractor, in the Hopfbifurcation theorem and its applications. Marsden, J.E., McCracken, M. (ed.), pp. 368-381. Berlin, Heidelberg, New York: Springer 1976
[4]Williams, R.F.: The structure of Lorenz attractors. Preprint (1977)
[5]McLaughlin, J.B., Martin, P.C.: Transition to turbulence in a statistically stressed fluid system. Phys. Rev. A12, 186-203 (1975) · doi:10.1103/PhysRevA.12.186
[6]Curry, J.H.: Transition to turbulence in finite-dimensional approximations to the Boussinesq equations. Ph. D. Thesis, University of California, Berkeley (1976)
[7]Smale, S.: A structurally stable differentiable homeomorphism with an infinite number of periodic points. Proc. Int. Symp. Nonlinear Vibrations, Vol. II (1961); Izdat. Akad. Nauk. Ukrain SSR, Kiev (1963)
[8]Smale, S.: Differentiable dynamical systems. Bull. Am. Math. Soc.73, 747-817 (1967) · Zbl 0202.55202 · doi:10.1090/S0002-9904-1967-11798-1
[9]Denjoy, A.: Sur les courbes défines par les équations différentielles à la surface du tore. J. Math. ser 9,11, 333-375 (1932)
[10]Ruelle, D., Takens, F.: On the nature of turbulence. Commun. Math. Phys.20, 167-192 (1971);23, 343-344 (1971) · Zbl 0223.76041 · doi:10.1007/BF01646553
[11]Gottschalk, W.H., Hedlund, G.A.: Topological dynamics, Vol. 36 (revised ed.). Providence, R.I.: Am. Math. Soc., Colloquium Pub. 1968
[12]Nitecki, Z.: Differentiable dynamics. An introduction to the orbit structure of diffeomorphisms. Cambridge, Mass.: M.I.T. Press 1971
[13]Robbins, K.A.: A new approach to subcritical instability and turbulent transitions in a simple dynamo. Math. Proc. Cambridge Phil. Soc.
[14]Creveling, H.F., DePaz, J.F., Baladi, J.V., Schoenhals, R.J.: Stability characteristics of a single phase free convection loop. J. Fluid Mech.67, 65-84 (1975) · Zbl 0312.76029 · doi:10.1017/S0022112075000171
[15]Marsden, J.E., McCracken, M.: The Hopf bifurcation and its applications. Berlin, Heidelberg, New York: Springer 1976
[16]Ruelle, D.: The Lorenz attractor and the problem of turbulence. Proc. Conf. Quantum Dynamics Models and Mathematics, Bielefeld (1975)
[17]Guckenheimer, J., Oster, G., Ipaktchi, A.: The dynamics of density dependent population models. J. Math. Biol.4, 101-147 (1977)