Hausdorff dimension for some hyperbolic attractors with overlaps and without finite Markov partition

Abstract

In this paper some families of skew product self-maps $F$ on the square are considered. The main example is a family forming a two-dimensional analogue of the tent map family. According to the assumptions made in this paper these maps are almost injective. This means that the points of the attractor having more than one inverse image form a set of measure zero for all interesting measures. It may be that $F$ does not have a finite Markov partition. The Hausdorff dimension of the attractor is computed.