Lyapunov spectrum of Markov and Euclid trees

We study the Lyapunov exponents Λ(x) for Markov dynamics as a function of path determined by x∈RP1 on a binary planar tree, describing the Markov triples and their 'tropical' version-Euclid triples. We show that the corresponding Lyapunov spectrum is [0,ln⁡φ], where is the golden ratio, an...

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Bibliographic Details
Published in:Nonlinearity 2017-12, Vol.30 (12), p.4428-4453
Main Authors: Spalding, K, Veselov, A P
Format: Article
Language:English
Subjects:
Farey tree
Lyapunov spectrum
Markov numbers
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Summary:We study the Lyapunov exponents Λ(x) for Markov dynamics as a function of path determined by x∈RP1 on a binary planar tree, describing the Markov triples and their 'tropical' version-Euclid triples. We show that the corresponding Lyapunov spectrum is [0,ln⁡φ], where is the golden ratio, and prove that on the Markov-Hurwitz set X of the most irrational numbers the corresponding function ΛX is monotonically increasing and in the Farey parametrization is convex.
ISSN:0951-7715
1361-6544
DOI:10.1088/1361-6544/aa88ff