Local Dimensions and Quantization Dimensions in Dynamical Systems

Abstract

Let $$\mu $$ be a Borel probability measure generated by a hyperbolic recurrent iterated function system defined on a nonempty compact subset of $$\mathbb R^k$$ . We study the Hausdorff and the packing dimensions, and the quantization dimensions of $$\mu $$ with respect to the geometric mean error. The results establish the connections with various dimensions of the measure $$\mu $$ and generalize many known results about local dimensions and quantization dimensions of measures.