Self-similar sequences and universal scaling of dynamical entropies

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 54, Issue 5, 1996, Pages 5561-5566

  Freund, Jan ^a   Ebeling, Werner ^a   Rateitschak, Katja ^a  

^a HUMBOLDT UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000970729     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.54.5561     Document Type: Article

References (38)

1. V M. Alekseev and M V. Yakobson, Phys. Rep.75, 287 (1981).
2. W. Ebeling and G. Nicolis, Chaos, Solitons Fractals2, 635 (1992).
3. A. Rényi, Probability Theory (North-Holland, Amsterdam, 1970).
4. W. Ebeling and T. Pöschel, Europhys. Lett.26, 241 (1994).
5. W. Li, Physica A43, 5240 (1991).
6. R F. Voss and J. Clarke, J. Accoust. Soc.63, 258 (1978).
7. V S. Anishchenko, W. Ebeling and A B. Neiman, Chaos, Solitons Fractals4, 69 (1994).
8. H E. Stanley, S V. Buldyrev, A L. Goldberger, Z D. Goldberger, S. Havlin, R N. Mantegna, S M. Ossadnik, C.-K. Peng and M. Simons, Physica A205, 214 (1994).
9. H. Herzel and I. GroΒe, Physica A216, 518 (1995).
10. C E. Shannon, Bell Syst. Tech. J.27, 379 (1948).
11. A I. Khinchin, Mathematical Foundations of Information Theory (Dover Publ., New York, 1957).
12. A O. Schmitt, H. Herzel and W. Ebeling, Europhys. Lett.23, 303 (1993).
13. T. Pöschel, W. Ebeling and H. Rosé, J. Stat. Phys.80, 1443 (1995).
14. B. McMillan, Ann. Math. Stat.24, 196 (1953).
15. A. Kolmogorov, Dokl. Akad. Nauk SSSR119, 861 (1958).
16. Ya. G. Sinai, Dokl. Akad. Nauk SSSR124, 768 (1959).
17. F. Ledrappier and L.-S. Young, Ann. Math.122, 509 (1985);
18. F. Ledrappier and L.-S. Young, Ann. Math.122, 540 (1985).
19. L. Gatlin, Information Theory and the Living System (Columbia Univ. Press, New York, 1972).
20. G. Gy$$̋orgyi and P. Szépfalusy, Phys. Rev. A31, 3477 (1985).
21. P. Grassberger, Int. J. Theor. Phys.25, 907 (1986).
22. P. Szépfalusy and G. Gy$$̋orgyi, Phys. Rev. A33, 2825 (1986).
23. P. Szépfalusy, Phys. Scr.T25, 226 (1989).
24. A. Csordás, G. Gy$$̋orgyi, P. Szépfalusy and T. Tél, Chaos3, 31 (1993).
25. W. Ebeling and G. Nicolis, Europhys. Lett.14, 191 (1991).
26. M J. Feigenbaum, J. Stat. Phys.19, 25 (1978).
27. W. Ebeling, J. Freund and K. Rateitschak, Int. J. Bifurcation Chaos6, 611 (1996).
28. T. Gramss, Phys. Rev. E50, 2616 (1994).
29. I. Procaccia, S. Thomae and C. Tressor, Phys. Rev. A35, 1884 (1987).
30. M R. Schroeder, Fractals, Chaos, Power Laws (Freeman, New York, 1991).
31. M. R. Schroeder, Number Theory in Science and Communication, Springer Series in Information Sciences, 2nd enlarged ed. (Springer, Berlin, 1986).
32. A. Lindenmayer, J. Theor. Biol.18, 280 (1968).
33. K. Rateitschak, J. Freund, and W. Ebeling, in Entropy and Entropy Generation: Fundamentals and Applications, edited by J. S. Shiner (Kluwer, Dordrecht, 1996).
34. W. Hilberg, Frequenz44, 243 (1990).
35. S K. Ma, Modern Theory of Critical Phenomena (Benjamin, New York, 1976).
36. K G. Wilson, Rev. Mod. Phys.47, 773 (1975).
37. C. Beck and F. Schlögl, Thermodynamics of Chaotic Systems (Cambridge University Press, Cambridge, 1993).
38. H. Herzel, W. Ebeling and A O. Schmitt, Phys. Rev. E50, 5061 (1994).