Abstract
A classical theorem of Peixoto qualitatively characterizes, on the two-dimensional unit ball, the limit sets of structurally stable flows defined by ordinary differential equations. Peixoto’s density theorem further shows that such flows are typical in the sense that structurally stable systems form an open dense set in the space of all continuously differentiable flows.
In this note, we discuss the problem of explicitly finding the limit sets of structurally stable planar flows.
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Acknowledgments
We thank the referees’ helpful suggestions and insightful comments. D. Graça was partially funded by FCT/MCTES through national funds and co-funded EU funds under the project UIDB/50008/2020. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 731143.
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Graça, D.S., Zhong, N. (2021). Computability of Limit Sets for Two-Dimensional Flows. In: De Mol, L., Weiermann, A., Manea, F., Fernández-Duque, D. (eds) Connecting with Computability. CiE 2021. Lecture Notes in Computer Science(), vol 12813. Springer, Cham. https://doi.org/10.1007/978-3-030-80049-9_48
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DOI: https://doi.org/10.1007/978-3-030-80049-9_48
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