Table of Contents:
  • Motivated by the Invariant Subspace Problem, we describe explicitly the closed subspace H 2 generated by the limit points in the H 2 norm of the orbit of a thin Blaschke product B under composition operators C φ induced by non-elliptic automorphisms. This description exhibits a surprising connection to model spaces. Finally, we give a constructive characterization of the C φ-eigenfunctions in H p for 1≤p≤∞. © 2011 Elsevier Inc.