Mathematics – Dynamical Systems
Scientific paper
2004-11-16
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.
Dutkay Dorin E.
Jorgensen Palle E. T.
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