On simultaneous linearization of diffeomorphisms of the sphere
type: Item
instance of: scholarly article
title: On simultaneous linearization of diffeomorphisms of the sphere
zbMATH Open document ID: 1113.37038
author: D. Dolgopyat
author: Raphaël Krikorian
published in: Duke Mathematical Journal
publication date: 2007-03-12T00:00:00Z
review text: Small smooth random perturbations \(f_1,\dots, f_m\) of rotations \(R_1,\dots ,R_m\) generating SO\(_{d+1}\), \(d\geq 2\), are considered. It is shown that a necessary and sufficient condition for the zero Lyapunov exponent of the associated random walk is that \(\{f_{\alpha}\}\) can be linearized simultaneously. As a consequence it follows that if \(d\) is even and \(f_\alpha\) are sufficiently close to \(R_\alpha\) and preserve volume, then \(\{f_\alpha\}\) is ergodic.
reviewed by: Katarina Janková
Mathematics Subject Classification ID: 37H15
Mathematics Subject Classification ID: 37C85
Mathematics Subject Classification ID: 70H08
zbMATH DE Number: 5132699
zbMATH Keywords: random rotation
zbMATH Keywords: Lyapunov exponent
zbMATH Keywords: ergodicity
zbMATH Keywords: perturbations
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5132699