Abstract
Procedures which estimate the noisiness of complicated, aperiodic data are outlined here and considered in the context of transitional fluid flow, although similar questions arise in many other fields1,2. Because this is the initial formulation of these ideas only qualitative results are presented; any attempt to develop quantitative measures of randomness will be postponed until more testing and refinement of the procedures have been completed.
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References
Guckenheimer, J. Lect. Math. Life Sci. 10, 1–47 (1978).
Brillinger, D. R., Guckenheimer, J., Guttorp, P. & Oster, G. Lect. Math. Life Sci. 13, 65–90 (1981).
Swinney, H. L. & Gollub, J. (eds) Hydrodynamic Instabilities and the Transition to Turbulence (Springer, New York, 1981).
Landau, L. & Lifshitz, E. M. Fluid Mechanics (Pergamon, Oxford, 1959).
Ruelle, D. & Takens, F. Comm. Math. Phys. 20, 167–192 (1971).
Libchaber, A. & Maurer, J. Nonlinear Phenomena and Phase Transitions (ed. T. Riste) (Geilo Nato School, in the press).
Gollub, J. P. & Benson, S. V. J. Fluid. Mech. 100, 449–470 (1980).
Eckmann, J.-P. Rev. mod. Phys. 53, 643–654 (1981).
Greenside, H. S., Ahlers, G., Hohenberg, P. C. & Walden, R. W. Physica D (in the press).
Guckenheimer, J., Moser, J. & Newhouse, S. Dynamical Systems (Birkhäuser, Boston, 1980).
Ruelle, D. Ann. N.Y. Acad. Sci. 316, 408–416 (1979).
Packard, N. H., Crutchfield, J. P., Farmer, J. D. & Shaw, R. S. Phys. Rev. Lett. 45, 712–716 (1980).
Froehling, H., Crutchfield, J. P., Farmer, J. D., Packard, N. H. & Shaw, R. S. Physica 3 D, 605–617 (1981).
Takens, F. in Dynamical Systems and Turbulence, Warwick 366–381 (Springer, New York, 1981).
Hirsch, M. W. Differential Topology (Srpinger, New York, 1976).
Smale, S. Bull. Am. math. Soc. 73, 747–817 (1967).
Henon, M. Comm. Math. Phys. 50, 69–78 (1976).
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Guckenheimer, J. Noise in chaotic systems. Nature 298, 358–361 (1982). https://doi.org/10.1038/298358a0
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DOI: https://doi.org/10.1038/298358a0
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