Orbits of non-elliptic disc automorphisms

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 $1\le p\le \infty$.

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