Fock-and-Mather-Nonlin-Revised.pdf (753.73 kB)
Download fileMarkov numbers, Mather's beta-function and stable norm
journal contribution
posted on 2019-09-24, 10:24 authored by A. Sorrentino, Alexander VeselovAlexander VeselovV. 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].
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