Generic Homeomorphisms have the Pseudo-Orbit Tracing Property

DOI10.2307/2048270zbMath0713.58025OpenAlexW4235883910MaRDI QIDQ3198575

Kenzi Odani

Publication date: 1990

Full work available at URL: https://doi.org/10.2307/2048270

zbMATH Keywords

topological stabilitypseudo-orbit tracing propertytolerance stabilitygeneric homeomorphisms

Mathematics Subject Classification ID

Related Items (22)

Periodic number for Anosov maps ⋮ On the genericity of the shadowing property for conservative homeomorphisms ⋮ Periodic orbits and chain-transitive sets of \(C^1\)-diffeomorphisms ⋮ On the periodic orbits, shadowing and strong transitivity of continuous flows ⋮ Recurrence, rigidity, and shadowing in dynamical systems ⋮ Tolerance stability conjecture revisited ⋮ Weak shadowing for discrete dynamical systems on nonsmooth manifolds ⋮ Theory of pseudo-orbit shadowing in dynamical systems ⋮ S-limit shadowing is generic for continuous Lebesgue measure-preserving circle maps ⋮ Shadowing is generic -- a continuous map case ⋮ Shadowing is generic on various one-dimensional continua with a special geometric structure ⋮ On genericity of shadowing in one dimension ⋮ Defect-controlled numerical methods and shadowing for chaotic differential equations ⋮ s-limit shadowing is \(\mathcal C^0\)-dense ⋮ Generic Homeomorphisms Have no Smallest Attractors ⋮ On the predictability of discrete dynamical systems ⋮ Invariant measures for typical continuous maps on manifolds ⋮ Generic Homeomorphisms have the Pseudo-Orbit Tracing Property ⋮ Topological aspects of incompressible flows ⋮ Shadowing is generic on dendrites ⋮ On the dynamics of generic maps on the Cantor set ⋮ Scrambled sets and chain recurrence points of generic graph maps

Cites Work

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• Manifolds with transverse fields in euclidean space
• A remark on the topological entropy of homeomorphisms
• Consequences of topological stability
• Homology theory and dynamical systems
• On semi-stability for diffeomorphisms
• Generic Homeomorphisms have the Pseudo-Orbit Tracing Property
• Structurally stable diffeomorphisms are dense
• Obstructions to the smoothing of piecewise-differentiable homeomorphisms

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