Gallardo Gutiérrez, Eva A.Gorkin, PamelaSuárez, Daniel2023-06-202023-06-2020120022-247X10.1016/j.jmaa.2011.10.048https://hdl.handle.net/20.500.14352/43772Motivated 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-phi, induced by non-elliptic automorphisms. This description exhibits a surprising connection to model spaces. Finally, we give a constructive characterization of the C-phi-eigenfunctions in H-p for 1 <= p <= infinity. (C) 2011 Elsevier Inc. All rights reserved.engjournal articlehttp://www.sciencedirect.com/science/article/pii/S0022247X11009905http://www.sciencedirect.com/restricted access517Blaschke productsInvariant subspacesEigenfunctions of composition operatorsAnálisis matemático1202 Análisis y Análisis Funcional