On topological classification of \(A\)-diffeomorphisms of surfaces
type: Item
instance of: scholarly article
title: On topological classification of \(A\)-diffeomorphisms of surfaces
zbMATH Open document ID: 0984.37020
DOI: 10.1023/A:1009573706584
published in: Journal of Dynamical and Control Systems
publication date: 2002-05-14T00:00:00Z
review text: This paper is a review of results obtained by the author and related to the topological classification of discrete dynamical systems (cascades) defined on an orientable smooth closed surface \({\mathcal A}_g\) of genus \(g\geq 0\). Topics are: 1) topological classification of one-dimensional basic sets via automorphisms of fundamental groups, 2) representation of one-dimensional basic sets by hyperbolic homeomorphisms, 3) structural stability and asymptotic behaviour of invariant manifolds of \(A\)-diffeomorphisms, 4) topological classification of Morse-Smale diffeomorphisms with a finite set of heteroclinic trajectories, 5) topological classification of structurally stable diffeomorphisms with one-dimensional basic sets.
Mathematics Subject Classification ID: 37C15
Mathematics Subject Classification ID: 37D15
Mathematics Subject Classification ID: 37E30
Mathematics Subject Classification ID: 37C29
Mathematics Subject Classification ID: 37D05
Mathematics Subject Classification ID: 37C20
zbMATH DE Number: 1475294
zbMATH Keywords: \(A\)-diffeomorphisms
zbMATH Keywords: orientable closed surface
zbMATH Keywords: fundamental group
zbMATH Keywords: hyperbolic homeomorphism
zbMATH Keywords: invariant manifold
zbMATH Keywords: basic set
author: V. Z. Grines
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
Recommended article: Q3450938
Recommended article: The diffeomorphism classification of non-simply connected Dolgachev surfaces.
Recommended article: On Topological Classification of Morse–Smale Diffeomorphisms
Recommended article: The classification of maps of nonorientable surfaces
Recommended article: On topological classification of diffeomorphisms on 3-manifolds with two-dimensional surface attractors and repellers
Recommended article: Q4289013
Recommended article: Topological classification of \(\mathbb{Z}_ p^ m\) actions on surfaces.
Recommended article: On topological classification of Morse–Smale diffeomorphisms on the sphere S n (n > 3)
Recommended article: Topological classification of Morse-Smale diffeomorphisms with finite set of heteroclinic trajectories on surfaces
Recommended article: On a topological classification of diffeomorphisms on 3-manifolds with two-dimensional surface attractors and repellers
description: scientific article; zbMATH DE number 1475294