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Infinitesimal Actions of \(\mathbf {R}^2\) Around Isolated Fixed Points in the Plane

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Abstract

We study infinitesimal smooth actions of \(\mathbf {R}^2\) (pairs of commuting vector fields) in the neighborhood of a fixed point on a surface, with special emphasis on the case where the action is tangent to the identity and the fixed point surrounded by an orbit of dimension two. We give conditions guaranteeing the topological and smooth equivalence of such actions.

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Acknowledgments

The author thanks Betrand Deroin, Jessica Jaurez, Jesús Muciño and Laura Ortiz for helpful conversations and the referee for his/her thorough reading, comments and suggestions. Funded by PAPIIT-UNAM (Mexico) grant IN108214.

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  1. Instituto de Matemáticas, Unidad Cuernavaca, Universidad Nacional Autónoma de México, A.P. 273-3 Admon. 3, Cuernavaca, Morelos, 62251, Mexico

    Adolfo Guillot

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  1. Adolfo Guillot
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Correspondence to Adolfo Guillot.

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Guillot, A. Infinitesimal Actions of \(\mathbf {R}^2\) Around Isolated Fixed Points in the Plane. Qual. Theory Dyn. Syst. 15, 433–451 (2016). https://doi.org/10.1007/s12346-016-0203-2

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