Local Dimensions and Quantization Dimensions in Dynamical Systems

Authors

Mrinal Kanti Roychowdhury, The University of Texas Rio Grande Valley
Bilel Selmi

Document Type

Article

Publication Date

10-2020

Abstract

Let μ be a Borel probability measure generated by a hyperbolic recurrent iterated function system defined on a nonempty compact subset of Rk. 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.

Comments

© 2020, Mathematica Josephina, Inc. Original published version available at https://doi.org/10.1007/s12220-020-00537-5

Recommended Citation

Roychowdhury, M.K., Selmi, B. Local Dimensions and Quantization Dimensions in Dynamical Systems. J Geom Anal (2020). https://doi.org/10.1007/s12220-020-00537-5

Publication Title

The Journal of Geometric Analysis

DOI

10.1007/s12220-020-00537-5