Composition laws on the Fricke surface and Markov triples
A. Muhammed Uluda\u{g}, Esra \"Unal Y{\i}lmaz
TL;DR
This paper explores composition laws on the Fricke surface and its double, revealing how these laws relate to solutions involving Markov triples, thus advancing understanding of their algebraic structure.
Contribution
It introduces new composition laws on the Fricke surface and its double, connecting these to Markov triples and expanding the algebraic framework.
Findings
Identified composition laws on the Fricke surface.
Linked the double Fricke surface to squares of Markov triples.
Enhanced understanding of algebraic structures related to Markov triples.
Abstract
We determine some composition laws related to the Fricke surface and the "double" Fricke surface. This latter surface admits the squares of Markov triples as its solutions.
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Taxonomy
TopicsOptimization and Search Problems · Mathematical Dynamics and Fractals