2017/02/05 by Jesús Hernández Serda, Serda, Jesús Hernández
Mathematics · #FOS: Mathematics #History and Theory of Mathematics #Mathematical Dynamics and Fractals #Mathematics and Applications #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1702.01448
openalex publication_date 2017/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.