Integrated wavelets on fractal sets. I. The correlation dimension

and

Published under licence by IOP Publishing Ltd
, , Citation J -M Ghez and S Vaienti 1992 Nonlinearity 5 777 DOI 10.1088/0951-7715/5/3/010

0951-7715/5/3/777

Abstract

The authors define the integrated wavelet transform of a measure on a set J and, using the thermodynamic formalism, they rigorously show that, for a large class of dynamical systems, it gives the correlation dimension of J. They recover qualitatively the same result analysing the Mellin transform of the wavelet. They apply this method to the numerical analysis of some hyperbolic and nonhyperbolic invariant sets.

Export citation and abstract BibTeX RIS

10.1088/0951-7715/5/3/010