Closed subspaces which are attractors for representations of the Cuntz   algebras
  We analyze the structure of co-invariant subspaces for representations of the Cuntz algebras O_N for N = 2,3,..., N < infinity, with special attention to the representations which are associated to orthonormal and tight-frame wavelets in L^2(R) corresponding to scale number N. 
Palle E. T. Jorgensen