Further scaling properties for circle maps
type: Item
instance of: scholarly article
title: Further scaling properties for circle maps
zbMATH Open document ID: 0579.58026
DOI: 10.1007/BF00418119
author: Dieter Mayer
published in: Letters in Mathematical Physics
publication date: 1984-01-01T00:00:00Z
review text: Universal scaling properties for circle maps which for rotation numbers \(\rho\) algebraic of degree two have been found recently by several groups are generalized to actions of the group \({\mathbb{Z}}^{k-1}\) on the circle. If the rotation numbers of their generators \(f_ 1,...,f_{k-1}\) are fixed or periodic points of the Perron-Jacobi algorithm and are therefore algebraic numbers of degree \(k>2\) then the corresponding action shows a universal behaviour under certain iterations independent of the special form of the \(f_ i's\). A renormalization group transformation is established which accounts for this behaviour and which in the case \(k=2\) reduces exactly to the known transformation for circle maps. A more elaborate version of this work has appeared in J. Stat. Phys. 38, 785-803 (1985).
Mathematics Subject Classification ID: 37-XX
Mathematics Subject Classification ID: 57S25
Mathematics Subject Classification ID: 11J70
zbMATH DE Number: 3927955
zbMATH Keywords: renormalization group transformation
zbMATH Keywords: \({\mathbb{Z}}^ h\) actions on the circle
zbMATH Keywords: Universal scaling properties for circle maps
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf00418119
OpenAlex ID: W1994500728
description: scientific article; zbMATH DE number 3927955