INTEGRATED WAVELETS ON FRACTAL SETS .1. THE CORRELATION DIMENSION

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