SOLVING THE INVERSE FRACTAL PROBLEM FROM WAVELET ANALYSIS

We report on a wavelet-based technique for solving the inverse fractal problem. We show that one can uncover a dynamical system which leaves invariant a given fractal object from the space scale arrangement of its wavelet transform modulus maxima. Our purpose is illustrated on Be moulli invariant measures of linear as well as non-linear <<cookie-cut ters>>. Application to period-doubling dynamical systems at the onset of chaos is reported.