Local dimensions and quantization dimensions in dynamical systems

2019/02/03 by Roychowdhury, Mrinal Kanti, Selmi, Bilel
#94A34 #Dynamical Systems (math.DS) #FOS: Mathematics #Primary 37A50 #Secondary 28A80

paper · doi:10.48550/arxiv.1902.00938

Abstract

Let μ 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 μ with respect to the geometric mean error. The results establish the connections with various dimensions of the measure μ, and generalize many known results about local dimensions and quantization dimensions of measures.

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