A monodromy criterion for a type of degenerate system defined by the sum of two homogeneous vector fields. (English) Zbl 1391.34064

Huang, Tusen; Zhang, Lijun

Rocky Mt. J. Math. 47, No. 7, 2255-2275 (2017).

The authors study the monodromy problem for a differential system with a degenerate singular point at the origin and defined by the sum of two homogeneous vector fields. The monodromy problem for this type of systems have been studied previously in several works. A monodromy criteron is given for such systems using the blow-up technique and a classification theorem. The criterion is applied to an ilustrative example showing that the results obtained improve known previous results.

Reviewer: Jaume Giné (Lleida)

MSC:

34C05

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations

Keywords:

planar degenerate system; monodromy criterion; blow-up technique