Estimaci\'on de la dimensi\'on de Hausdorff por dimensi\'on de conteo por cajas y dimensi\'on de informaci\'on

TL;DR

This paper explores relationships between different fractal dimensions, specifically Hausdorff, box-counting, and information dimensions, and applies these concepts to estimate the dimension of the Henon attractor.

Contribution

It establishes bounds between Hausdorff, box-counting, and information dimensions and demonstrates their application to the Henon attractor.

Findings

Box-counting dimension is an upper bound for Hausdorff dimension.

Information dimension is an upper bound for Hausdorff dimension.

The dimension of the Henon attractor is estimated using box-counting dimension.

Abstract

In this article, the Hausdorff dimension is estimated using the box-counting dimension and the information dimension. It is shown that the former is an upper bound for the Hausdorff dimension, while the latter is a lower bound for the box-counting dimension, and that the information dimension is an upper bound for the Hausdorff dimension. Additionally, the dimension of the Henon attractor is estimated using the box-counting dimension.