# A Multidimensional Gauss Map

## TL;DR

This paper explores higher-dimensional generalizations of the classical Gauss Map, investigating their potential to reveal new arithmetic and algebraic properties of irrational numbers through their dynamical behavior.

## Contribution

It introduces multidimensional Gauss Maps and discusses their possible connections to number theory, posing questions and conjectures about their arithmetic significance.

## Key findings

- Proposes higher-dimensional Gauss Map generalizations
- Suggests potential links to algebraic properties of irrationals
- Raises open questions and conjectures in the field

## Abstract

The classical Gauss Map is a piecewise continuous map from the unit interval to itself. From this map we retrieve the continued fraction expansion of irrational numbers and its dynamical properties give information about some arithmetic and algebraic properties of irrational numbers. In this notes we will explore some generalizations of the Gauss Map to higher dimensions and pose some questions and conjectures about the arithmetic/algebraic information that these maps may carry.