# The Hausdorff dimension of multiply Xiong chaotic sets

## TL;DR

This paper constructs a special type of chaotic set with full Hausdorff dimension in certain dynamical systems, demonstrating complex chaotic behavior with maximal fractal complexity.

## Contribution

It introduces a multiply Xiong chaotic set with full Hausdorff dimension within multiply proximal cells for the full shift and Gauss systems, advancing understanding of chaos in these systems.

## Key findings

- Constructed multiply Xiong chaotic set with full Hausdorff dimension
- Set contained in multiply proximal cells for full shift and Gauss systems
- Demonstrated existence of highly complex chaotic sets in these systems

## Abstract

We construct a multiply Xiong chaotic set with full Hausdorff dimension everywhere that is contained in some multiply proximal cell for the full shift over finite symbols and the Gauss system respectively.