Fock-and-Mather-Nonlin-Revised.pdf (753.73 kB)
Markov numbers, Mather's beta-function and stable norm
Version 2 2019-02-11, 09:22
Version 1 2019-02-11, 09:22
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].
History
School
- Science
Department
- Mathematical Sciences
Published in
NonlinearityVolume
32Issue
6Pages
2147-2156Citation
SORRENTINO, A. and VESELOV, A.P., 2019. Markov numbers, Mather's beta-function and stable norm. Nonlinearity, 32(6), 2147-2156Publisher
London Mathematical SocietyVersion
- AM (Accepted Manuscript)
Publisher statement
This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/Acceptance date
2019-02-05Publication date
2019-05-08ISSN
0951-7715Publisher version
Language
- en