Local phase portraits through the Newton diagram of a vector field

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2015-06

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Ciencias Integradas

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Center

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https://hdl.handle.net/10272/25454

Abstract

The Newton diagram and, in particular, the lowest-degree quasi-homogeneous terms of an analytic planar vector field allow us to determine the existence of characteristic orbits and separatrices of an isolated singular point. We give an easy algorithm for obtaining the local phase portrait near the origin of a bi-dimensional differential system and we provide several examples.

Keywords

Ecuaciones diferenciales; Degenerate vector fields; Phase portraits; Monodromy of vector fields; Monodromy; Separatrices; Quasi-homogeneous vector field

Unesco Subjects

1206.02 Ecuaciones Diferenciales

Bibliographic citation

Algaba, A., Checa, I., García, C., & Reyes, M. (2015). Local phase portraits through the Newton diagram of a vector field. Acta Mathematica Sinica, English Series, 31(6), 1015–1034. https://doi.org/10.1007/s10114-015-3663-4

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