Methods from multiscale theory and wavelets applied to non-linear dynamics

Details Methods from multiscale theory and wavelets applied to non-linear dynamics Methods from multiscale theory and wavelets applied to non-linear dynamics

2004-11-16

arxiv.org/abs/math/0411371v3

Wavelets, Multiscale Systems and Hypercomplex Analysis (D. Alpay, ed.), Oper. Theory Adv. Appl., vol. 167, Birkh\~A?user, Bost

Mathematics

Dynamical Systems

survey. v2: We have polished the writing and corrected some of the cross references and citations; and v2 has an acknowledgmen

Scientific paper

We show how fundamental ideas from signal processing, multiscale theory and wavelets may be applied to non-linear dynamics. The problems from dynamics include iterated function systems (IFS), dynamical systems based on substitution such as the discrete systems built on rational functions of one complex variable and the corresponding Julia sets, and state spaces of subshifts in symbolic dynamics. Our paper serves to motivate and survey our recent results in this general area. Hence we leave out some proofs, but instead add a number of intuitive ideas which we hope will make the subject more accessible to researchers in operator theory and systems theory.

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