An estimate on the Hausdorff dimension of stable sets of non-uniformly hyperbolic horseshoes

TL;DR

This paper proves that the Hausdorff dimension of stable sets in non-uniformly hyperbolic horseshoes is less than two, providing insight into their geometric complexity.

Contribution

It establishes a strict upper bound on the Hausdorff dimension of stable sets in a class of non-uniformly hyperbolic dynamical systems.

Findings

Hausdorff dimension of stable sets is less than two

Provides bounds on geometric complexity of non-uniformly hyperbolic horseshoes

Advances understanding of fractal geometry in dynamical systems

Abstract

We show that the Hausdorff dimension of stable sets of non-uniformly hyperbolic horseshoes is strictly smaller than two.