Dynamics in the Szegő class and polynomial asymptotics
We introduce the Szegő class, Sz(E), for an arbitrary Parreau–Widom set E ⊂ ℝ and study the dynamics of its elements under the left shift. When the direct Cauchy theorem holds on ℂ\E, we show that to each J ∈ Sz(E) there is a unique element J′ in the isospectral torus, T E , so that the left-shifts of J are asymptotic to the orbit {J′ m } on T E . Moreover, we show that the ratio of the associ
