Bijectivity and trapping regions for complex continued fraction transformation

2016/08/23 by Zydney, Adam
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1608.06351

Abstract

This paper provides some preliminary results on the dynamics of certain complex continued fractions. After establishing some general number theoretic results, we explore the dynamics of the natural extension map associated to a specific complex continued fraction algorithm (the "diamond" algorithm). We prove that this map has a bijectivity domain that is a subset of a trapping region for the map and, moreover, that both these sets have a "finite product structure" arising from a finite partition specific to the particular algorithm.

Related

• Finite partitions for several complex continued fraction algorithms
• Serendipitous decompositions of higher-dimensional continued fractions
• Periodic points in complex continued fractions by J. Hurwitz
• Continued fraction expansions for complex numbers - a general approach
• Complex continued fractions, Kleinian and extremal theory for cusp excursions