Stability of orbit spaces of endomorphisms
type: Item
instance of: scholarly article
title: Stability of orbit spaces of endomorphisms
zbMATH Open document ID: 0885.58063
DOI: 10.1007/BF02677460
published in: Manuscripta Mathematica
publication date: 1997-07-23T00:00:00Z
full work available at URL: https://eudml.org/doc/156288
review text: In this paper results concerning hyperbolic sets of diffeomorphisms are extended to \(C^1\) endomorphisms. Among other things it is proved that a hyperbolic set of a \(C^1\) endomorphism is weakly structurally stable and weakly topologically stable. Also some \(\Omega\) stability theorems are extended to endomorphisms satisfying some nondegeneracy conditions. In the theory put forward, the orbit space of the map considered plays an important role.
reviewed by: M. Farkas
Mathematics Subject Classification ID: 37D99
Mathematics Subject Classification ID: 37C75
Mathematics Subject Classification ID: 37A99
zbMATH DE Number: 1038290
zbMATH Keywords: \(C^ 1\) endomorphisms
zbMATH Keywords: hyperbolic sets of diffeomorphisms
zbMATH Keywords: stability theorems
author: Peidong Liu
MaRDI profile type: Publication
cites work: Q3729587
cites work: Periodic points and chaotic functions in the unit interval
cites work: Neighborhoods of hyperbolic sets
cites work: Smooth ergodic theory of random dynamical systems
cites work: A proof of the \(C^ 1\) stability conjecture
cites work: On semi-stability for diffeomorphisms
cites work: On the \(C^ 1\Omega\)-stability conjecture
cites work: The space of dynamical systems with the \(C^ 0\)-topology
cites work: Anosov endomorphisms
cites work: On Ω-stability and structural stability of endomorphisms satisfying Axiom A
cites work: Ergodic Attractors
cites work: Ergodic theory for axiom A endomorphisms
cites work: Exact endomorphisms of a Lebesgue space
cites work: Endomorphisms of Compact Differentiable Manifolds
cites work: Q3931654
cites work: Q3772940
description: scientific article; zbMATH DE number 1038290