ANALYTICITY OF DIMENSIONS FOR HYPERBOLIC SURFACE DIFFEOMORPHISMS.

In this note we give a simple proof that the Hausdorff dimension of the basic set for a real analytic Smale horseshoe map depends analytically on the transformation. This method is based on the use of dynamical zeta functions. We prove analogous statements for the value of the pointwise dimension of the measure of maximal entropy and then use this to address an interesting question raised by Damanik and Gorodetski. [ABSTRACT FROM AUTHOR]