On equivalent definitions of the correlation dimension for a probability measure

Journal of Statistical Physics

Volumn 86, Issue 3-4, 1997, Pages 707-720

  Guerin, Charles Antoine ^a   Holschneider, Matthias ^a  

^a CENTRE DE PHYSIQUE THÉORIQUE   (France)

Author keywords

Correlation dimension; Fractal measure

Indexed keywords

EID: 0031065037     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02199116     Document Type: Article

References (7)

1. C. Allain and M. Cloitre, Optical diffraction on fractals, Phys. Rev. B 33(5):3566-3569 (1985).
2. C. A. Guerin and M. Holschneider, Scattering on fractal measures, J. Phys. A: Math. Gen. 29:1-17 (1996).
3. M. Holschneider, Fractal wavelet dimension and localisation, Commun. Math. Phys. 160:457-473 (1994).
4. R. Ketzmerick, G. Petschel, and T. Geisel, Slow decay of temporal correlations in quantum systems with Cantor spectral, Phys. Rev. Lett. 69(5):695-698 (1992).
5. Ya, B. Pesin, On rigorous mathematical definition of the correlation dimension and generalized spectrum for dimension, J. Stat. Phys. 71(3/4):529-547 (1993).
6. M. Reed and B. Simon, Methods of Modern Mathematical Physics: Functional Analysis (Academic Press, New York, 1980).
7. W. Rudin, Analyse réelle et complexe (Masson, Paris, 1978).