On the regularity of integrable conformal structures invariant under Anosov systems
type: Item
instance of: scholarly article
title: On the regularity of integrable conformal structures invariant under Anosov systems
zbMATH Open document ID: 1072.37026
author: Rafael de la Llave
author: Victoria Sadovskaya
published in: Discrete and Continuous Dynamical Systems
publication date: 2005-04-11T00:00:00Z
review text: The paper deals with the volume-preserving Anosov diffeomorphism \(f: M\to M\), where \(M\) is an \(m\)-dimensional \(C^\infty\) compact manifold. Let \(E\subset TM\) be a subbundle invariant under \(Df\), \(\dim E= d\geq 2\). Roughly speaking, a conformal structure \(C_x\), \(x\in M\), is a linear operator on \(E_x\) with the norm \[ \| C_x\|= \sup_{0\neq v\in E+x} {\langle C_x v,v\rangle\over\| v\|^2}. \] With respect to these norms, the \(L^p\) spaces of the conformal structures can be defined. The authors prove that if such a structure is in \(L^p\) for sufficiently large \(p\), then it is continuous.
reviewed by: A. Klíč
Mathematics Subject Classification ID: 37D20
Mathematics Subject Classification ID: 37F15
Mathematics Subject Classification ID: 30C65
Mathematics Subject Classification ID: 42B20
Mathematics Subject Classification ID: 37J10
zbMATH DE Number: 2155026
zbMATH Keywords: conformal structures
zbMATH Keywords: Anosov systems
zbMATH Keywords: Sobolev spaces
zbMATH Keywords: stable and unstable foliation
MaRDI profile type: Publication
full work available at URL: dcds.2005.12.377
OpenAlex ID: W2095031043
DOI: 10.3934/DCDS.2005.12.377
description: scientific article; zbMATH DE number 2155026