A dimension formula for endomorphisms - The Belykh family

In [11] we considered a class of hyperbolic endomorphisms and asked the question whether there exists a physical motivated invariant measure (SRB-measure) and if so we gave a criterion when the map is invertible on a set of full measure. In this work we want to consider a particular example of this class - in fact a 3-parameter family of those - and proof that a.s. the criterion is fulfilled. From this it follows that the Young formulae for the Hausdorff dimension of the SRB-measure holds