# Local dimensions and quantization dimensions in dynamical systems

## TL;DR

This paper investigates the relationships between Hausdorff, packing, and quantization dimensions of measures generated by hyperbolic recurrent iterated function systems, extending known results in the field.

## Contribution

It generalizes existing results by establishing connections between various measure dimensions and quantization errors for hyperbolic recurrent iterated function systems.

## Key findings

- Established links between Hausdorff, packing, and quantization dimensions.
- Generalized known results on local and quantization dimensions.
- Provided new insights into the dimensions of measures generated by complex 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.