One-parameter flows with the pseudo-orbit tracing property
type: Item
instance of: scholarly article
title: One-parameter flows with the pseudo-orbit tracing property
zbMATH Open document ID: 0545.58037
DOI: 10.1007/BF01507750
author: Motomasa Komuro
published in: Monatshefte für Mathematik
publication date: 1984-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/178202
review text: A notion of the pseudo-orbit tracing property (abbr. POTP) for one- parameter flows on compact metric spaces is discussed. The strong POTP, the strong finite POTP, the normal POTP, the weak POTP and the finite POTP for flows are defined, and the relation between these POTP's is clarified; these are equivalent to each other for flows with no fixed points, but that is not true for flows with fixed points. Moreover, the following is proved; (i) The restriction to the nonwandering set of a flow with the strong POTP has the strong POTP. (ii) If an expansive flow on the nonwandering set has the finite POTP, the flow splits into the finite union of subsystems with topological transitivity. (iii) Every isometric flow with the finite POTP is minimal. (iv) The direct product of flows with the strong POTP does not necessarily have the finite POTP.
Mathematics Subject Classification ID: 37D99
Mathematics Subject Classification ID: 37C10
Mathematics Subject Classification ID: 54H20
zbMATH DE Number: 3868293
zbMATH Keywords: pseudo-orbit tracing property
zbMATH Keywords: one-parameter flows
MaRDI profile type: Publication
cites work: Homeomorphisms without the pseudo-orbit tracing property
cites work: On homeomorphisms with pseudo-orbit tracing property
cites work: Periodic Orbits for Hyperbolic Flows
cites work: Expansive one-parameter flows
cites work: Abstract ω-Limit Sets, Chain Recurrent Sets, and Basic Sets for Flows
cites work: Hyperbolicity and Cycles
cites work: Q3321140
cites work: Topological \(\Omega\)-stability of axiom A flows with no- \(\Omega\)- explosions
cites work: Expansive Homeomorphisms and Topological Dimension
cites work: Q3942090
cites work: Q3264374
cites work: The \(\Omega\)-stability theorem for flows
cites work: Differentiable dynamical systems
cites work: Q4188476
OpenAlex ID: W1969406138
description: scientific article; zbMATH DE number 3868293