On the wavelet formalism for multifractal analysis

Chaos

Volumn 11, Issue 4, 2001, Pages 858-863

  Murguia J S ^a   Urías, Jesús ^a  

^a UNIVERSIDAD AUTÓNOMA DE SAN LUIS POTOSÍ   (Mexico)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035649439     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1423282     Document Type: Article

References (9)

1. T. C. Halsey, M. H. Jensen, L. P. Kadanoff, I. Procaccia, and B. I. Shraiman, "Fractal measures and their singularities: The characterization of strange sets," Phys. Rev. A 33, 1141-1151 (1986).
2. H. G. E. Hentschel and I. Procaccia, Physica D 13, 34 (1983).
3. J. F. Muzy, E. Bacry, and A. Arneodo, "Wavelets and multifractal formalism for singular signals: applications to turbulence data," Phys. Rev. Lett. 67, 3515-3518 (1991).
4. E. Bacry, J. F. Muzy, and A. Arneodo, "Singularity spectrum of fractal signals from wavelet analysis: exact results," J. Stat. Phys. 70, 635-674 (1993).
5. H. Federer, Geometric Measure Theory (Springer-Verlag, Berlin, 1969).
6. Ya. B. Pesin, Dimension Theory in Dynamical Systems. Contemporary Views and Applications (University of Chicago Press, Chicago, 1997).
7. Roughly speaking, a conformal axiom-A diffeomorphism is at every point equally expanding in the expanding directions and equally contracting in the contracting directions. See for instance, Ya. B. Pesin and V. Sadovskaya, "Multifractal analysis of conformal axiom A flows," Commun. Math. Phys. 216, 277-312 (2001).
8. J. F. Muzy, E. Bacry, and A. Arneodo, "The multifractal formalism revisited with wavelets," I. J. Bifurcations Chaos 4, 245-302 (1994).
9. J. M. Ghez and S. Vaienti, "On the wavelet analysis for multifractal sets," J. Stat. Phys. 57, 415-420 (1989).