Hausdorff dimension, strong hyperbolicity and complex dynamics
type: Item
instance of: scholarly article
title: Hausdorff dimension, strong hyperbolicity and complex dynamics
zbMATH Open document ID: 0954.37019
author: S. Friedland
author: Gunter Ochs
published in: Discrete and Continuous Dynamical Systems
publication date: 2000-08-16T00:00:00Z
review text: This paper is roughly divided into three parts. In the first part the authors give sufficient conditions on an Axiom A surface diffeomorphism that possesses a unique Gibbs measure whose Hausdorff dimension is equal to the Hausdorff dimension of its nonwandering set. In the second part the authors introduce the notion of strong Axiom A diffeomorphisms of a manifold with \(n= \dim M> 2\) and show that the notion of strong hyperbolicity is structurally stable. In the third part they study the dynamics of some proper polynomial maps \(f: \mathbb{C}^2\to \mathbb{C}^2\) which extend to holomorphic self-maps of \(\mathbb{C} P^2\).
Mathematics Subject Classification ID: 37D40
Mathematics Subject Classification ID: 37C70
Mathematics Subject Classification ID: 37D20
zbMATH DE Number: 1492533
zbMATH Keywords: structural stability
zbMATH Keywords: Axiom A surface diffeomorphism
zbMATH Keywords: Gibbs measure
zbMATH Keywords: Hausdorff dimension
zbMATH Keywords: strong Axiom A diffeomorphisms
zbMATH Keywords: strong hyperbolicity
zbMATH Keywords: polynomial maps
zbMATH Keywords: holomorphic self-maps
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: dcds.1998.4.405
OpenAlex ID: W2052649885
DOI: 10.3934/DCDS.1998.4.405
description: scientific article; zbMATH DE number 1492533