Quantization dimensions for the bi-Lipschitz recurrent Iterated function systems

TL;DR

This paper estimates the quantization dimensions of probability measures supported on limit sets of bi-Lipschitz recurrent iterated function systems, using spectral radius under the strong open set condition.

Contribution

It provides a new estimation method for quantization dimensions based on spectral radius for measures on complex fractal structures.

Findings

Quantization dimensions are explicitly estimated in terms of spectral radius.

Results apply to measures supported on limit sets of bi-Lipschitz recurrent IFS.

The approach extends understanding of measure complexity in fractal geometry.

Abstract

In this paper, the quantization dimensions of the Borel probability measures supported on the limit sets of the bi-Lipschitz recurrent iterated function systems under the strong open set condition in terms of the spectral radius have been estimated.