  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.
