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- W4285594860 abstract "It is well known that linear vector fields defined in $mathbb{R}^n$ can not have limit cycles, but this is not the case for linear vector fields defined in other manifolds. We study the existence of limit cycles bifurcating from a continuum of periodic orbits of linear vector fields on manifolds of the form $(mathbb{S}^2)^m times mathbb{R}^n$ when such vector fields are perturbed inside the class of all linear vector fields. The study is done using the averaging theory. We also present an open problem concerning the maximum number of limit cycles of linear vector fields on $(mathbb{S}^2)^m times mathbb{R}^n$." @default.
- W4285594860 created "2022-07-16" @default.
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- W4285594860 date "2022-07-14" @default.
- W4285594860 modified "2023-09-27" @default.
- W4285594860 title "Limit cycles of linear vector fields on $(mathbb{S}^2)^m times mathbb{R}^n$" @default.
- W4285594860 doi "https://doi.org/10.48550/arxiv.2207.07006" @default.
- W4285594860 hasPublicationYear "2022" @default.
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