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Please use this identifier to cite or link to this item: https://dspace.lboro.ac.uk/2134/36930

Title: Markov numbers, Mather's beta-function and stable norm
Authors: Sorrentino, A.
Veselov, A.P.
Issue Date: 2019
Publisher: London Mathematical Society
Citation: SORRENTINO, A. and VESELOV, A.P., 2019. Markov numbers, Mather's beta-function and stable norm. Nonlinearity, In Press.
Abstract: V. Fock [7] introduced an interesting function ψ(x), x ∈ R related to Markov numbers. We explain its relation to Federer-Gromov’s stable norm and Mather’s β-function, and use this to study its properties. We prove that ψ and its natural generalisations are differentiable at every irrational x and non-differentiable otherwise, by exploiting the relation with length of simple closed geodesics on the punctured or oneholed tori with the hyperbolic metric and the results by Bangert [3] and McShane-Rivin [23].
Description: This paper is in closed access until it is published.
Version: Accepted for publication
URI: https://dspace.lboro.ac.uk/2134/36930
Publisher Link: https://iopscience.iop.org/journal/0951-7715
ISSN: 0951-7715
Appears in Collections:Closed Access (Maths)

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