2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73810We 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.13 pages, LaTeX2e "amsart" document classDynamical SystemsFunctional Analysis60G18 (Primary) 42C40, 46G15, 42A65, 28A50, 30D05, 47D07, 37F20 (Secondary)text