Weak shadowing for discrete dynamical systems on nonsmooth manifolds
type: Item
instance of: scholarly article
title: Weak shadowing for discrete dynamical systems on nonsmooth manifolds
zbMATH Open document ID: 1024.37014
DOI: 10.1016/S0022-247X(03)00186-0
author: Marcin Mazur
published in: Journal of Mathematical Analysis and Applications
publication date: 2003-07-30T00:00:00Z
review text: The author gives another proof of the result of \textit{R. M. Corless} and \textit{S. Yu. Pilyugin} [J. Math. Anal. Appl. 189, 409-423 (1995; Zbl 0821.58036)], which proved that weak shadowing is a \(C^{0}\) generic property in the space of discrete dynamical systems on a compact smooth manifold \(M\). The presented new proof does not assume that \(M\) has a differential structure and works even for systems on some compact metric spaces that are not manifold, such as a Hilbert cube and a Cantor set.
reviewed by: Ladislav Adamec
Mathematics Subject Classification ID: 37C50
zbMATH DE Number: 1956889
zbMATH Keywords: shadowing
zbMATH Keywords: discrete dynamical systems
zbMATH Keywords: pseudo-trajectory
zbMATH Keywords: homogeneity
zbMATH Keywords: generic property
MaRDI profile type: Publication
cites work: Q3135846
cites work: Stretching the Oxtoby-Ulam Theorem
cites work: Dynamics of topologically generic homeomorphisms
cites work: Q4297122
cites work: \(\omega\)-limit sets for axiom A diffeomorphisms
cites work: Approximate and real trajectories for generic dynamical systems
cites work: Transformation groups and \(C^ *\)-algebras
cites work: Homogeneity of infinite products of manifolds with boundary
cites work: Some facts about homogeneity properties
cites work: Hyperbolic homeomorphisms and bishadowing
cites work: Foundational Essays on Topological Manifolds, Smoothings, and Triangulations. (AM-88)
cites work: Q3286041
cites work: Affine structures in 3-manifolds. V: The triangulation theorem and Hauptvermutung
cites work: Filtrations, Decompositions, and Explosions
cites work: Generic Homeomorphisms have the Pseudo-Orbit Tracing Property
cites work: Q4342768
cites work: Q3374449
cites work: Q4331453
cites work: Shadowing in dynamical systems
cites work: Shadowing is generic
cites work: An Improved Closing Lemma and a General Density Theorem
cites work: Beyond hyperbolicity
cites work: Q5621780
cites work: Q4337982
cites work: Q4188476
cites work: Manifolds with transverse fields in euclidean space
cites work: Homogeneity of Infinite Products of Manifolds with Boundary
cites work: Q3785633
description: scientific article; zbMATH DE number 1956889