On the uniqueness of measures of full Hausdorff dimension for some compact invariant sets
Abstract. The Hausdorff dimension of a "general Sierpinski cartpet" was found by McMullen and Bedford and the uniqueness of the measure of full Hausdorff dimension in some cases was proved by Kenyon and Peres. We extend these results by considering a general Sierpinski carpet represented by a shift of finite type. Applying results of Ledrappier, Young and Shin, we study the Hausdorff dimension of a such a general Sierpinski carpet for the case when there is a saturated compensation function. We give some conditions under which a general Sierpinski carpet has a unique measure of full Hausdorff dimension and study the properties of the unique measures.