Abstract
Motivated by the Invariant Subspace Problem, we describe explicitly the closed subspace H2 generated by the limit points in the H2 norm of the orbit of a thin Blaschke product B under composition operators Cφ induced by non-elliptic automorphisms. This description exhibits a surprising connection to model spaces. Finally, we give a constructive characterization of the Cφ-eigenfunctions in Hp for 1⩽p⩽∞.
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