Integrated wavelets on fractal sets. I. The correlation dimension
- 1 May 1992
- journal article
- Published by IOP Publishing in Nonlinearity
- Vol. 5 (3) , 777-790
- https://doi.org/10.1088/0951-7715/5/3/010
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.Keywords
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