Abstract: The question of spectral analysis for deterministic chaos generated by interval maps is not well understood in the literature. In this talk, using the special property of exponential growth of the total variation of the iterates of chaotic interval maps, we are able to derive analytical and asymptotic properties of the Fourier coefficients of such iterates when n (i.e., the number of iterations) grows large. We can then use the usual L^p theory to derive further properties of the Fourier coefficients.

Similar properties for the wavelet coefficients are also obtained when multi-resolution analysis is used to study the iterates of a chaotic interval map. Concrete examples and estimates are presented when a Haar wavelet basis is used.

This talk is based on papers recently written by G. Chen, S_B. Hsu, Y. Huang and M. Roque-Sol.