Superpositions of multifractals: Generators of phase transitions in the generalized thermodynamic formalism

Journal of Statistical Physics

Volumn 82, Issue 3-4, 1996, Pages 1063-1080

  Radons, Günter ^a   Stoop, Ruedi ^b  

^a UNIVERSITY OF KIEL   (Germany)

^b UNIVERSITY OF ZURICH   (Switzerland)

Author keywords

Generalized thermodynamic formalism; Multifractals; Phase transitions; Projections of fractal measures

Indexed keywords

EID: 0001590466     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02179802     Document Type: Article

References (29)

1. P. Mattila, Ann. Acad. Sci. Fenn. A I 1:227 (1975).
2. G. Radons, Physica A 191:532 (1992).
3. G. Radons, J. Stat. Phys. 72:227 (1993).
4. G. Radons, Phys. Rev. Lett. 75:2518 (1995).
5. O. E. Lanford, in Statistical Mechanics and Mathematical Problems, A. Lenard, ed. (Springer, Berlin, 1973).
6. D. Katzen and I. Procaccia, Phys. Rev. Lett. 58:1169 (1986).
7. P. Grassberger, in Proceedings Workshop on Dynamics on Fractals and Hierarchies of Critical Exponents (Orsay, 1986).
8. P. Cvitanović, in XVth International Colloquium on Group Theoretical Methods in Physics, R. Gilmore, ed. (World Scientific, Singapore, 1987).
9. D. Ruelle, Thermodynamic Formalism ( Addison-Wesley, Reading, Massachusetts, 1978).
10. H. G. E. Hentschel and I. Procaccia, Physica 8D:435 (1983).
11. T. C. Halsey, M. H. Jensen, L. P. Kadanoff, I. Procaccia, and B. Shraiman, Phys. Rev. A 33:1141 (1986).
12. J. P. Eckmann and I. Procaccia, Phys. Rev. A 34:659 (1986).
13. H. G. Schuster, Deterministic Chaos, 2nd ed. (VCH, Weinheim, 1989).
14. T. Tél, Z. Naturforsch. 43a:1154 (1988).
15. R. Stoop, Z. Naturforsch 46a:1117 (1991).
16. Z. Kovács and T. Tél, Phys. Rev. A 45:2270 (1992).
17. J. Peinke, J. Parisi, O. E. Roessler, and R. Stoop, Encounter with Chaos (Springer, Berlin, 1992).
18. Ch. Beck and F. Schögl, Thermodynamics of Chaotic Systems (Cambridge University Press, Cambridge, 1993).
19. J. Feder, Fractals (Plenum Press, New York, 1988).
20. K. Falconer, Fractal Geometry (Wiley, Chichester, 1990).
21. M. Kohmoto, Phys. Rev. A 37:1345 (1988).
22. R. Stoop and J. Parisi, Phys. Rev. A 43:1802 (1991).
23. R. Stoop, J. Parisi, and H. Brauchli, Z. Naturforsch 46a:642 (1991).
24. R. Stoop and J. Parisi, Phys. Lett. A 161:67 (1991).
25. M. E. Fisher and D. R. Nelson, Phys. Rev. Lett. 32:1350 (1975).
26. W. Gebhardt and U. Krey, Phasenübergänge und kritische Phänomene (Vieweg, Braunschweig, 1980).
27. P. Grassberger and I. Procaccia, Phys. Rev. Lett. 50:346 (1983).
28. E. Ott, C. Grebogi, and J. A. Yorke, Phys. Lett. A 135:343 (1989).
29. G. Radons, Z. Naturforsch 49a:1219 (1994).