2022/08/30 by А. П. Веселов, Veselov, A. P. · 1 citation
Computer Science · #11D25 #11H55 #Data Management and Algorithms #Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2208.14184
openalex publication_date 2022/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Recently Valentin Ovsienko introduced a ``shadow" version of the celebrated Markov triples as the solutions of certain version of Markov equation over dual numbers. We will discuss similar question for the Mordell Diophantine equation X2+Y2+Z2=2XYZ+1. We will see that the shadows of the special solution (1,1,1) can be described using the original Conway topograph of the values of binary quadratic forms. The shadows of other Mordell triples will be written explicitly in terms of the corresponding solutions of Pell's equation. Their growth along the paths on the Conway topograph is described in terms of the Lyapunov function of the Euclid tree.