Full attracting sets of annulus maps which are inverse limits of circles

In 1986 Marcy Barge showed that the full attracting sets of maps similar to Smaleʹs horseshoe map are homeomorphic to inverse limits of the unit interval. Recently, the author extended Bargeʹs results to a more general class of maps of the plane. In this paper we show that similar maps of the annulus and the solid torus have full attracting sets which are homeomorphic to inverse limits of cirles.