Topological proof for the alexander-orbach conjecture

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

Volumn 56, Issue 3, 1997, Pages 2437-2446

  Milovanov, Alexander V ^a  

^a Russian Academy of Sciences   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000227788     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.56.2437     Document Type: Article

References (35)

1. J. Feder, Fractals (Plenum, New York, 1988).
2. M B. Isichenko, Rev. Mod. Phys.64, 961 (1992).RMPHAT
3. S. Alexander and R. Orbach, J. Phys. (France) Lett.43, L625 (1982).JPSLBO
4. T. Nakayama, K. Yakubo, and R. Orbach, Rev. Mod. Phys.66, 381 (1994).RMPHAT
5. H. Takayasu, Fractals in the Physical Sciences (Manchester University Press, Manchester, 1990)
6. A. Le Mèhautè, Fractal Geometries: Theory and Applications (CRC, Boca Raton, FL, 1991).
7. Y. Gefen, A. Aharony, and S. Alexander, Phys. Rev. Lett.50, 77 (1983).PRLTAO
8. B B. Mandelbrot, The Fractal Geometry of Nature (Freeman, New York, 1983).
9. B. O’Shaughnessy and I. Procaccia, Phys. Rev. Lett.54, 455 (1985).PRLTAO
10. B. O’Shaughnessy and I. Procaccia, Phys. Rev. A32, 3073 (1985).PLRAAN
11. S. Havlin and D. Ben-Avraham, Adv. Phys.36, 695 (1987).ADPHAH
12. L M. Zelenyi, A V. Milovanov, and G. Zimbardo, in New Perspectives of the Earth’s Magnetotail, Geophysics Monograph, edited by A. Nishida, D. N. Baker, and S. W. H. Cowley (American Geophysical Union, Washington, DC, in press).
13. M. Giona and H E. Roman, Physica A185, 87 (1992).PHYADX
14. A V. Milovanov, and L M. Zelenyi, in Physics of the Magnetopause, Geophysics Monograph No. 90, edited by P. Song, B. U. O. Sonnerup, and M. F. Thomsen (American Geophysical Union, Washington, DC, 1995), p. 357.
15. E. Clement, R. Kopelman, and L M. Sander, J. Stat. Phys.65, 919 (1991).JSTPBS
16. A V. Milovanov, Russ. J. Astron. Zh. 71, 360 (1994) [Astron. Rep.38, 314 (1994)].ATROES
17. R. Orbach, Physica D38, 266 (1989).PDNPDT
18. A V. Milovanov (unpublished)
19. A V. Milovanov and L M. Zelenyi, in Physics of Space Plasma, Series 14, edited by T. Chang (Massachusetts Institute of Technology, Cambridge, 1996), p. 373
20. L M. Zelenyi and A V. Milovanov, Russ. J. Geomagn. Aeronom.37, 1 (1997).
21. M. Schroeder, Fractals, Chaos, Power Laws (Freeman, New York, 1991).
22. A. Coniglio, J. Phys. A15, 3829 (1982).JPHAC5
23. A V. Milovanov and G. Zimbardo (unpublished).
24. M W. Hirsch, Differential Topology (Springer-Verlag, New York, 1976).
25. Ch. Nash and S. Sen, Topology and Geometry for Physicists (Academic, London, 1983)
26. A T. Fomenko and D B. Fuks, A Course of the Homotopic Topology (Nauka, Moscow, 1989).
27. L M. Zelenyi and A V. Milovanov, Russ. J. Astron. Zh. 73, 805 (1996) [Astron. Rep.40, 734 (1996)].ATROES
28. B A. Dubrovin, S P. Novikov, and A T. Fomenko, The Modern Geometry. Methods and Applications (Nauka, Moscow, 1986).
29. Yu. G. Borisovich, N. M. Bliznyakov, Ya. A. Izrailevich, and T. N. Fomenko, Introduction to Topology (Nauka, Moscow, 1995).
30. Yu. B. Rumer and M. Sh. Ryvkin, Thermodynamics, Statistical Physics, and Kinetics (Nauka, Moscow, 1977).
31. V G. Boltyanskyi and V A. Efremovich, Descriptive Topology (Nauka, Moscow, 1983).
32. L. Schwartz, Analyse Mathématique. Cours Professé à L’Ecole Polytechnique, Paris (Hermann, Paris, 1967)
33. S. M. Nikol’skyi, A Course of Mathematical Analysis (Nauka, Moscow, 1983).
34. A T. Fomenko, Differential Geometry and Topology. Additional Chapters (Moscow State University Press, Moscow, 1983).
35. J M. Normand, H J. Herrmann, and M. Hajjar, J. Stat. Phys.52, 441 (1988).