Growth of values of binary quadratic forms and Conway rivers
Dynamical Systems
2020-05-06 v3 Number Theory
Abstract
We study the growth of the values of binary quadratic forms on a binary planar tree as it was described by Conway. We show that the corresponding Lyapunov exponents as a function of the path determined by are twice the values of the corresponding exponents for the growth of Markov numbers \cite{SV}, except for the paths corresponding to the Conway rivers, when The relation with Galois results about continued fraction expansions for quadratic irrationals is explained and interpreted geometrically.
Keywords
Cite
@article{arxiv.1703.00038,
title = {Growth of values of binary quadratic forms and Conway rivers},
author = {K. Spalding and A. P. Veselov},
journal= {arXiv preprint arXiv:1703.00038},
year = {2020}
}
Comments
A few typos and the claim in Proposition 5 about semidefinite case are corrected