Cocycles' stability for partially hyperbolic systems
type: Item
instance of: scholarly article
title: Cocycles' stability for partially hyperbolic systems
zbMATH Open document ID: 0853.58082
author: Anatole Katok
author: A. Kononenko
published in: Mathematical Research Letters
publication date: 1997-01-05T00:00:00Z
review text: The cohomological equation for an unknown function \(\varphi\) on a space \(X\) reads \(\varphi(x) - h(x) + h(f(x)) = 0\), where \(h\) is the given transfer function on \(X\) and \(f\) is a given transformation \(X \to X\). A solution \(\varphi\) is also called a coboundary and two functions are cohomologous if their difference is a coboundary. Results on this type of cohomology of particular importance are the Livshitz theorems on hyperbolic diffeomorphisms of manifolds. There are related results for some non-hyperbolic systems too: the present paper establishes Livshitz-type theorems for partially hyperbolic systems. For a large class of discrete systems and flows the space of Hölder coboundaries is closed and admits a natural geometrical description. The authors also derive transitivity results for the pair of stable and unstable foliations.
Mathematics Subject Classification ID: 37D99
Mathematics Subject Classification ID: 37C85
zbMATH DE Number: 913759
zbMATH Keywords: cocycles
zbMATH Keywords: stable foliations
zbMATH Keywords: partially hyperbolic systems
zbMATH Keywords: unstable foliations
reviewed by: Rainer Schimming
MaRDI profile type: Publication
full work available at URL: mrl.1996.v3.n2.a6
OpenAlex ID: W2018782139
DOI: 10.4310/MRL.1996.V3.N2.A6
description: scientific article; zbMATH DE number 913759