A practical method to experimentally evaluate the Hausdorff dimension: An alternative phase-transition-based methodology

Chaos

Volumn 14, Issue 4, 2004, Pages 1004-1017

  Li, Jun ^a,b   Arneodo, Alain ^a,b   Nekka, Fahima ^a  

^a UNIVERSITÉ DE MONTRÉAL   (Canada)

^b UNIVERSITÉ DE LYON   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 15044361647     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1803435     Document Type: Article

References (36)

1. G. Peano, in Selected Works, edited by, H. C. Kennedy, (Toronto University Press, Toronto, 1973).
2. F. Hausdorff, Math. Ann. 79, 157 (1919).
3. A. S. Besicovitch, Math. Ann. 110, 321 (1935).
4. K. J. Falconer, The Geometry of Fractal Sets (Cambridge University Press, Cambridge, 1985).
5. J. P. Kahane, in Recent Progress in Fourier Analysis, edited by, I. Perse, and, J. L. Rubio di Francia, (North-Holland, Amsterdam, 1985), pp. 65-121.
6. A-N. Kolmogorov, Dokl. Akad. Nauk. SSSR 119, 861 (1958).
7. J. D. Farmer, E. Ott, and J. A. Yorke, Physica D 7, 153 (1983).
8. P. Grassberger and I. Procaccia, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.50.346 50, 346 (1983); P. Grassberger and I. Procaccia, Physica D 9, 189 (1983).
9. P. Grassberger and I. Procaccia, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.50.346 50, 346 (1983); P. Grassberger and I. Procaccia, Physica D 9, 189 (1983).
10. R. Badii and A. Politi, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett. 52.1661 52, 1661 (1984); R. Badii and A. Politi, J. Stat. Phys. 40, 725 (1985).
11. R. Badii and A. Politi, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett. 52.1661 52, 1661 (1984); R. Badii and A. Politi, J. Stat. Phys. 40, 725 (1985).
12. P. Grassberger, R. Badii, and A. Politi, J. Stat. Phys. 51, 135 (1988).
13. G. Grasseau, Ph.D. thesis, University of Bordeaux I, France, 1989.
14. F. Argoul, A. Arneodo, J. Elezgaray, G. Grasseau, and R. Murenzi, Phys. Rev. A 41, 5537 (1990).
15. L. V. Meisel, M. Johnson, and P. J. Cote, Phys. Rev. A 45, 6989 (1992).
16. The Science of Fractal Images, edited by, H. O. Peitgen, and, D. Saupe, (Springer-Verlag, New York, 1987).
17. R. F. Voss, Physica D 38, 362 (1989).
18. G. A. Edgar, Measures, Topology and Fractal Geometry (Springer-Verlag, Berlin, 1990).
19. S. Davies and P. Hall, Technical Report No. SRR 96-008, School of Mathematical Sciences, National Australian University, 1996.
20. B. Dubuc, J. F. Quiniou, C. Roques-Carmes, C. Tricot, and S. W. Zucker, Phys. Rev. A 39, 1500 (1989).
21. T. Higuchi, Physica D 46, 254 (1990).
22. N. P. Greis and H. P. Greenside, Phys. Rev. A 44, 2324 (1991).
23. W. Li, Int. J. Bifurcation Chaos Appl. Sci. Eng. 1, 583 (1991).
24. J. Schmittbuhl, J. P. Violette, and S. Roux, Phys. Rev. E 51, 131 (1995).
25. A. Scotti, C. Meneveau, and S. G. Saddoughi, Phys. Rev. E 51, 5594 (1995).
26. B. Lea-Cox and J. S. Y. Wang, Fractals 1, 87 (1993).
27. F. Nekka and J. Li, Chaos, Solitons Fractals 13, 1807 (2002).
28. J. Li and F. Nekka, Pattern Recogn. Lett. 24, 2723 (2003).
29. J. Li and F. Nekka, Chaos, Solitons Fractals 19, 35 (2004).
30. D. C. Champeney, Fourier Transforms and their Physical Applications (Academic, New York, 1973).
31. F. Nekka and J. Li, SIAM Proceedings, First Joint Meeting of CAIMS and SIAM, Montreal, Canada, June 2003.
32. B. B. Mandelbrot, Fractals: Form, Chance and Dimension (Freeman, San Francisco, 1977); B. B. Mandelbrot, The Fractal Geometry of Nature (Freeman, San Francisco, 1982).
33. B. B. Mandelbrot, Fractals: Form, Chance and Dimension (Freeman, San Francisco, 1977); B. B. Mandelbrot, The Fractal Geometry of Nature (Freeman, San Francisco, 1982).
34. J. Feder, Fractals (Pergamon, New York, 1988).
35. T. Vicsek, Fractal Growth Phenomena (World Scientific, Singapore, 1989).
36. J. Theiler, J. Opt. Soc. Am. A 7, 1055 (1990).