Flows with the (asymptotic) average shadowing property on three-dimensional closed manifolds

DOI10.1080/14689367.2011.604025zbMath1244.37018OpenAlexW2134507949MaRDI QIDQ3106380

Raquel Ribeiro, Alexander Arbieto

Publication date: 21 December 2011

Published in: Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/14689367.2011.604025

zbMATH Keywords

Anosov flowasymptotic average shadowingaverage shadowing

Mathematics Subject Classification ID

Approximate trajectories (pseudotrajectories, shadowing, etc.) in smooth dynamics (37C50)

Related Items (15)

Robustly chain transitive diffeomorphisms ⋮ Robust chain transitive vector fields ⋮ Vector fields with the asymptotic orbital pseudo-orbit tracing property ⋮ Asymptotic average shadowing property and chain transitivity for multiple flow systems ⋮ Divergence-free vector fields with average and asymptotic average shadowing property ⋮ Continuous semi-flows with the almost average shadowing property ⋮ \(\mathscr{M}\)-shadowing and transitivity for flows ⋮ Diffeomorphisms with \(C^1\)-stably average shadowing ⋮ Stable weakly shadowable volume-preserving systems are volume-hyperbolic ⋮ Chaos in a topologically transitive semi-flow ⋮ Multi-sensitivity, syndetical sensitivity and the asymptotic average- shadowing property for continuous semi-flows ⋮ Robustly chain transitive sets with orbital shadowing diffeomorphisms ⋮ Conservative flows with various types of shadowing ⋮ A note on decay of correlation implies chaos in the sense of Devaney ⋮ A type of the shadowing properties for generic view points

Cites Work

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• The asymptotic average-shadowing property and transitivity for flows
• Connecting invariant manifolds and the solution of the \(C^ 1\) stability and \(\Omega\)-stability conjectures for flows
• Periodic orbits and chain-transitive sets of \(C^1\)-diffeomorphisms
• Asymptotic average shadowing property on compact metric spaces
• A generic incompressible flow is topological mixing
• Shadowing is generic
• Orbital and weak shadowing properties
• Nonsingular star flows satisfy Axiom A and the no-cycle condition
• Vector fields with topological stability
• Diffeomorphisms with weak shadowing
• Perturbations of the derivative along periodic orbits
• Limit shadowing property
• Projective hyperbolicity and fixed points
• Recurrence and genericity
• Diffeomorphisms with the average-shadowing property on two-dimensional closed manifolds

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