Entropy formula and continuity of entropy for piecewise expanding maps

Abstract We consider some classes of piecewise expanding maps in finite dimensional spaces having invariant probability measures which are absolutely continuous with respect to Lebesgue measure. derive an entropy formula for such and, using this formula, we present sufficient conditions the continuity that parameter parametrized families maps. apply our results a classical one-dimensional family tent and two-dimensional arises as limit return when homoclinic tangency is unfolded by three diffeomorphisms.