Abstract
Arguments in favor of the nondifferentiability with respect to initial data of some functions associated with deterministic discrete-time dynamical systems are presented. A correspondence between a discrete-time dynamical system and a deterministic scattering model is found and used to interpret nondifferentiability conditions. A connection with random walks is also found.
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References
R. M. May,Nature 262:459 (1976).
E. Ott,Rev. Mod. Phys. 53:655 (1981).
J.-P. Eckmann and D. Ruelle,Rev. Mod. Phys. 57:617 (1985).
M. J. Feigenbaum,J. Stat. Phys. 19:25 (1978);21:669 (1979);Phys. Lett. A 74:375 (1979);Commun. Math. Phys. 77:65 (1980).
J. L. Kaplan, J. Mallet-Paret, and J. A. Yorke, University of Maryland, Preprint (1982).
J. D. Farmer, E. Ott, and J. A. Yorke,Physica 7D:105 (1983).
H. Kahn,Nucleonics 6:27 (1950).
J. P. Crutchfield, J. D. Farmer, and B. A. Huberman,Phys. Rep. 92:45 (1982).
H. Levy and F. Lessman,Finite Difference Equations (MacMillan, New York, 1961).
G. H. Hardy,Trans. Am. Math. Soc. 17:301 (1916).
A. Zygmund,Duke Math. J. 12:47 (1945).
R. E. A. C. Paley and N. Wiener,Fourier Trnsforms in the Complex Domain (American Mathematical Society, Providence, Rhode Island, 1934).
E. W. Montroll and M. F. Shlesinger, inNonequilibrium Phenomena. II. From Stochastics to Hydrodynamics, J. L. Lebowitz and E. W. Montroll, Eds. (North-Holland, New York, 1984).
T. Geisel and J Nierwetberg, inLecture Notes in Physics, Vol. 179 (Springer, New York, 1983), p. 93.
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Okniński, A. Chaos in discrete maps, deterministic scattering, and nondifferentiable functions. J Stat Phys 52, 577–594 (1988). https://doi.org/10.1007/BF01019718
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DOI: https://doi.org/10.1007/BF01019718