Quantization dimension and temperature function for recurrent self-similar measures

We determine the quantization dimension function for the image measure supported on a recurrent self-similar set of an ergodic Markov measure, and its relationship with the temperature function of the thermodynamic formalism arising in multifractal analysis is established.

► Quantization dimension for a recurrent self-similar measure is determined.
► The relation of quantization dimension with temperature function is established.
► It is an extension of a result given by Graf and Luschgy.