Infinite words with finite defect

In this paper, we provide a new characterization of uniformly recurrent words with finite defect based on a relation between the palindromic and factor complexity. Furthermore, we introduce a class of morphisms Pret closed under composition and we show that a uniformly recurrent word with finite defect is an image of a rich (also called full) word under a morphism of class Pret. This class is closely related to the well-known class P defined by Hof, Knill, and Simon; every morphism from Pret is conjugate to a morphism of class P.