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Lyapunov spectrum of Markov and Euclid trees

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journal contribution
posted on 12.01.2018, 14:11 authored by Kathryn Spalding, Alexander VeselovAlexander Veselov
© 2017 IOP Publishing Ltd & London Mathematical Society. We study the Lyapunov exponents Λ(x) for Markov dynamics as a function of path determined by x ∈ ℝP 1 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 φ is the golden ratio, and prove that on the MarkovHurwitz set X of the most irrational numbers the corresponding function Λ X is monotonically increasing and in the Farey parametrization is convex.

Funding

The work of K.S. was supported by the EPSRC as part of PhD study at Loughborough.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Nonlinearity

Volume

30

Issue

12

Pages

4428 - 4453

Citation

SPALDING, K. and VESELOV, A.P., 2017. Lyapunov spectrum of Markov and Euclid trees. Nonlinearity, 30(12), pp. 4428-4453.

Publisher

© IOP Publishing and London Mathematical Society

Version

AM (Accepted Manuscript)

Acceptance date

29/08/2017

Publication date

2017-11-09

Copyright date

2017

Notes

This is an author-created, un-copyedited version of an article published in Nonlinearity. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://doi.org/10.1088/1361-6544/aa88ff.

ISSN

0951-7715

eISSN

1361-6544

Language

en

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