Symbolic dynamics and entropy analysis of Feigenbaum limit sets

Chaos, Solitons and Fractals

Volumn 10, Issue 7, 1999, Pages 1135-1150

  Karamanos, K ^a   Nicolis, G ^a  

^a UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0012474428     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0960-0779(98)00095-2     Document Type: Article

References (31)

1. Nicolis, G., Introduction to Nonlinear Science. Cambridge University Press, Cambridge, 1995.
2. Hao B.-L., Chaos. World Scientific, Singapore, 1994.
3. Schuster, H. G., Deterministic Chaos. Physik-Verlag, 1984.
4. Nicolis, G. and Gaspard, P., Toward a probabilistic approach to complex systems. Chaos, Solitons & Fractals, 1994, 4(1), 41-57.
5. Khinchin, A. I., Mathematical Foundations of Information Theory. Dover, New York, 1957.
6. Kemeny, J. and Snell, L., Finite Markov Chains. Springer-Verlag, Berlin, 1976.
7. Thom, R., Paraboles et Catastrophes. Flammarion, Paris, 1983.
8. Nicolis, J. S., Chaos and Information Processing. World Scientific, Singapore, 1991.
9. Eckmann, J. P. and Ruelle, D., Ergodic theory of chaos and strange attractors. Rev. Mod. Phys., 1985, 57, 617.
10. Milnor, J. and Thurston, W., On iterated maps of the interval. In: Proceedings, University of Maryland, Vol. 1342, Dynamical Systems, ed. J. C. Alexander. Lecture Notes in Mathematics, Springer-Verlag, 1986-87, pp. 465-563 (and references therein).
11. de Groot, S. R. and Mazur, P., Non-Equilibrium Thermodynamics. Dover, New York, 1961.
12. Julia, G., Mémoire sur l'itération des fonctions rationelles. J. de Math. (Liouville) Ser., 1918, 7(14), 47-245, (The relevant theorem appears on p. 129ff).
13. Fatou, M. P., Sur les équations fonctionnelles. Bull. Soc. Math. France, 1919, 47, 161-271.
14. Fatou, M. P., Sur les équations fonctionnelles. Bull. Soc. Math. France, 1920, 48, 33-94, (also pp. 208-314).
15. Metropolis, N., Stein, M. L. and Stein, P. R., On finite limit sets for transformations on the unit interval. Journal of Combinatorial Theory, 1973, A15(1), 25-44.
16. Derrida, B., Gervois, A. and Pomeau, Y., Iteration of endomorphisms on the real axis and representation of numbers. Ann. Inst. Henri Poincaré, Section A: Physique Théorique, 1978, XXIX(3), 305-356.
17. Feigenbaum, M., Quantitative universality for a class of nonlinear transformations. J. Stat. Phys., 1978, 19, 25.
18. Feigenbaum, M., The universal metric properties of nonlinear transformations. J. Stat. Phys., 1979, 21, 669.
19. Grassberger, P., On the Hausdorff dimension of fractal attractors. J. Stat. Phys., 1981, 26(1), 173.
20. Fraser, S. and Kapral, R., Mass and dimension of Feigenbaum attractors. Phys. Rev., 1985, A31(3), 1687.
21. Grassberger, P., Toward a quantitative theory of self-generated complexity. Int. J. Theor. Phys., 1986, 25(9), 907.
22. Ebeling, W. and Nicolis, G., Entropy of symbolic sequences: the role of correlations. Europhys. Lett., 1991, 14(3), 191-196.
23. Ebeling, W. and Nicolis, G., Word frequency and entropy of symbolic sequences: a dynamical perspective. Chaos, Solitons & Fractals, 1992, 2, 635.
24. Nicolis, G., Rao, G., Rao, J. and Nicolis, C., Generation of spatially assymmetric, information-rich structures in far from equilibrium systems. In: Coherence and Chaos in Dynamical Systems, eds. P. L. Christiansen and R. D. Parmentier. Manchester University Press, 1988.
25. Nicolis, G., Nicolis, C. and Nicolis, J. S., Chaotic dynamics, Markov partitions and Zipf's law. J. Stat. Phys., 1989, 54(3/4), 915.
26. Freund, J., Ebeling, W. and Rateitschak, K., Self-similar sequences and universal scaling of dynamical entropies. Phys. Rev., 1996, E54(5), 5561-5566.
27. Rateitschak, K., Freund, J. and Ebeling, W., Entropy of sequences generated by nonlinear processes: the logistic map. In: Entropy and Entropy Generation, ed. J. S. Shiner. Kluwer Acad. Publ., 1996, pp. 11-26.
28. Freund, J. and Rateitschak, K., Entropy analysis of noise contaminated sequences. Int. Journ. of Bifurcation and Chaos, 1998, 8(5), 933.
29. Lindenmayer, A., J. Theor. Biology, 1968, 18, 280.
30. Mandelbrot, B. B., The Fractal Geometry of Nature. Freeman, San Franscisco, 1982.
31. Balakrishnan, V., Nicolis, G. and Nicolis, C., Recurrence time statistics in chaotic dynamics. I. Discrete time maps. J. Stat. Phys., 1997, 86, 191.