Growth of values of binary quadratic forms and Conway rivers

Autor:	Spalding, K., Veselov, A. P.
Rok vydání:	2017
Předmět:	Mathematics - Dynamical Systems Mathematics - Number Theory 11H55 34D08
Druh dokumentu:	Working Paper
DOI:	10.1112/blms.12156
Popis:	We study the growth of the values of binary quadratic forms $Q$ on a binary planar tree as it was described by Conway. We show that the corresponding Lyapunov exponents $\Lambda_Q(x)$ as a function of the path determined by $x\in \mathbb RP^1$ 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 $\Lambda_Q(x)=0.$ The relation with Galois results about continued fraction expansions for quadratic irrationals is explained and interpreted geometrically. Comment: A few typos and the claim in Proposition 5 about semidefinite case are corrected
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1703.00038 Zobrazit plný text záznamu View this record from Arxiv