Measures of maximal and full dimension for smooth maps

For a C-1 non-conformal repeller, this paper proves that there exists an ergodic measure of full Caratheodory singular dimension. For an average conformal hyperbolic set of a C-1 diffeomorphism, this paper constructs a Borel probability measure (with support strictly inside the repeller) of full Hausdorff dimension. If the average conformal hyperbolic set is of a C-1 +/-alpha; diffeomorphism, this paper shows that there exists an ergodic measure of maximal dimension.