The Markov Tree

Martin Aigner
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Martin Aigner: Freie Universität Berlin, Fachbereich Mathematik und Informatik Institut für Mathematik

Chapter 3 in Markov's Theorem and 100 Years of the Uniqueness Conjecture, 2013, pp 45-62 from Springer

Abstract: Abstract We begin here our journey through the mathematical world around Markov’s theorem, and the obvious way to start is to analyze the Markov equation and the Markov sequence M. So far, we do not even know whether there are infinitely many Markov numbers, but there is a wonderful and elegant device to see this and much more. We arrange the Markov triples in an infinite binary tree, the Markov tree. This is not only a convenient dataset, but it leads effortlessly to first results concerning the uniqueness conjecture. The Markov tree will be the main tool along the path to the proof of Markov’s theorem

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-00888-2_3

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DOI: 10.1007/978-3-319-00888-2_3

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