Wavelet constructions in non-linear dynamics
  We construct certain Hilbert spaces associated with a class of non-linear dynamical systems X. These are systems which arise from a generalized self-similarity, and an iterated substitution. We show that when a weight function W on X is given, then we may construct associated Hilbert spaces H(W) of L^2-martingales which have wavelet bases. 
Dorin Ervin Dutkay and Palle E.T. Jorgensen