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Statistical mechanics of multi-dimensional Cantor sets, Gödel theorem and quantum spacetime. (English) Zbl 0825.93012


MSC:

93A10 General systems
62P05 Applications of statistics to actuarial sciences and financial mathematics
82C03 Foundations of time-dependent statistical mechanics
Full Text: DOI

References:

[1] El Naschie, M. S., On turbulence and complex dynamics in a four-dimensional peano-Hilbert space, J. Franklin Inst., Vol. 330, 165-180 (1993) · Zbl 0825.93011
[2] El Naschie, M. S., Multidimensional Cantor sets and ergodic behaviour, Specul. Sci. and Technol.. Specul. Sci. and Technol., Proc. 13th World Congress on Computation and Applied Math., Vol. 2, 851-142 (1991), See also
[3] Kapitaniak, T., On strange nonchaotic attractors and their dimensions, Chaos, Solitons and Fractals, Vol. 1, 67-77 (1991) · Zbl 0739.58042
[4] Snell, J. L., Introduction to Probability (1989), McGraw-Hill: McGraw-Hill New York · Zbl 0676.60001
[5] Bosch, K., Elementare Einfuehrung in die Wahrscheinlichkeitsrechnung (1986), Vieweg: Vieweg Braunschweig
[6] Serra, R.; Zanarini, G., Complex Systems and Cognitive Processes (1990), Springer: Springer Berlin
[7] Wolfram, S., Statistical mechanics of cellular automata, Rev. Mod. Phys., Vol. 55, No. 3 (Nov. 3, 1983) · Zbl 1174.82319
[8] Chandler, D., Introduction to Modern Statistical Mechanics (1987), Oxford University Press: Oxford University Press New York
[9] Huang, K., Statistical Mechanics (1963), Wiley: Wiley New York
[10] Ebeling, W., Chaos-Ordnung-Information (1989), Harri Deutsch Verlag: Harri Deutsch Verlag Berlin
[11] Prigogine, I., From Being to Becoming (1980), Freeman: Freeman New York
[12] El Naschie, M. S., Stress, Stability and Chaos (1990), McGraw-Hill: McGraw-Hill London · Zbl 0729.73919
[13] Berge, P.; Pomeau, Y.; Vidal, C., L’Ordre Dans le Chaos (1984), Hermann: Hermann Paris · Zbl 0669.58022
[14] Duong-van, M., Instabilities, turbulence and physics of fixed points, (Mayer-Kress, G., Dimensions and Entropies in Chaotic Systems (1989), Springer: Springer Berlin), 171-178
[15] Paidoussis, M. P.; Moon, F. C., Nonlinear and chaotic elastic vibrations of a flexible pipe conveying fluid, J. Fluids Struct., 567-591 (1988)
[16] Held, G. A.; Jeffries, C. D., Characterization of chaotic instabilities in an electronhole plasma in Germanium, (Meyer-Kress, G., Dimensions and Entropies in Chaotic Systems (1988), Springer: Springer Berlin), 158-170
[17] Stewart, I., The Problems of Mathematics (1987), Oxford University Press: Oxford University Press Oxford · Zbl 0784.00012
[18] Rucker, R., Mind Tools (1987), Houghton Mifflin: Houghton Mifflin Boston, MA · Zbl 0702.00039
[19] El Naschie, M. S., Gödel, Cantor and modern nonlinear dynamics, (Proc. Int. Symp. Gödel’s Theorem. Proc. Int. Symp. Gödel’s Theorem, Université Pierre et Marie Curie, Paris, France, 27-29 May 1991, (1993), World Scientific: World Scientific Singapore), Chairman W. Wolkowski · Zbl 0825.93012
[20] Chaitin, G. J., Randomness and mathematical proof, Scient. Am., 47-52 (May 1975)
[21] El Naschie, M. S.; Kapitaniak, T., Soliton chaos models for mechanical and biological elastic chains, Phys. Lett. A., Vol. 147, 275-281 (1990)
[22] Smale, S., Differential dynamical systems, Bull. Am. Math. Soc., Vol. 73, 747-817 (1967) · Zbl 0202.55202
[23] El Naschie, M. S., Physics-like mathematics in four dimensions—implications for classical and quantum mechanics, (Ames, W. F.; van der Houwen, P. J., Computational and Applied Mathematics II (1992), Elsevier Science: Elsevier Science New York), 15-23 · Zbl 0771.58042
[24] El Naschie, M. S., On the uncertainty of information in quantum space-time, Chaos, Solitons and Fractals, Vol. 2, 91-94 (1992) · Zbl 0800.81004
[25] Ford, J., What is chaos, that we should be mindful of, (Davies, P., The New Physics (1989), Cambridge University Press), 348-372
[26] El Naschie, M. S., A note on Heisenberg’s uncertainty principle and Cantorian spacetime, Chaos, Solitons and Fractals, Vol. 2, 437-439 (1992) · Zbl 0771.58041
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