Shadowing is generic on dendrites

DOI10.3934/dcdss.2019142zbMath1439.37021OpenAlexW2907004995MaRDI QIDQ2305695

Jonathan Meddaugh, William Rea Brian, Brian E. Raines

Publication date: 13 March 2020

Published in: Discrete and Continuous Dynamical Systems. Series S (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdss.2019142

zbMATH Keywords

topological dynamicsdendritepseudo-orbitshadowingpseudo-orbit tracing property

Mathematics Subject Classification ID

Topological spaces of dimension (leq 1); curves, dendrites (54F50) Symbolic dynamics (37B10) Notions of recurrence and recurrent behavior in topological dynamical systems (37B20) Approximate trajectories, pseudotrajectories, shadowing and related notions for topological dynamical systems (37B65)

Related Items (5)

Shadowing as a structural property of the space of dynamical systems ⋮ Recurrence, rigidity, and shadowing in dynamical systems ⋮ Typical properties of interval maps preserving the Lebesgue measure ^* ⋮ Shadowing is generic on various one-dimensional continua with a special geometric structure ⋮ On genericity of shadowing in one dimension

Cites Work

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• Graph theoretic structure of maps of the Cantor space
• Shadowing is generic -- a continuous map case
• \(\omega\)-limit sets for axiom A diffeomorphisms
• Complex dynamics
• Weak shadowing for discrete dynamical systems on nonsmooth manifolds
• Shadowing is generic
• Approximate and real trajectories for generic dynamical systems
• s-limit shadowing is \(\mathcal C^0\)-dense
• Generic Homeomorphisms have the Pseudo-Orbit Tracing Property

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