Abstract
In this paper, we introduce the notion of the asymptotic orbital pseudo-orbit tracing property for a vector field X of a compact smooth manifold M. We show that if a vector field X has the \(C^1\) robust asymptotic orbital pseudo-orbit tracing property, then it is Anosov, and if a \(C^1\) generic vector field X has the asymptotic orbital pseudo-orbit tracing property, then it is Anosov. Moreover, we also show our results for divergence-free vector fields and Hamiltonian systems.
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Acknowledgements
The authors thank the referee for the careful reading and helpful comments that improved the quality of the paper.
Funding
Manseob Lee is supported by National Research Foundation of Korea (NRF) 2017R1A2B4001892 and Junmi Park is supported by Korea (NRF) 2017R1D1A1B03032148.
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Lee, M., Park, J. Vector Fields with the Asymptotic Orbital Pseudo-orbit Tracing Property. Qual. Theory Dyn. Syst. 19, 52 (2020). https://doi.org/10.1007/s12346-020-00388-z
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DOI: https://doi.org/10.1007/s12346-020-00388-z
Keywords
- Pseudo-orbit tracing
- Limit pseudo-orbit tracing
- Asymptotic orbital pseudo-orbit tracing
- Chain transitive
- Generic
- Anosov