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The global geometric properties of a class of homogeneous vector fields of degree two in \(R^3\). (Chinese) Zbl 0949.34022

The authors give some studies on quadratic homogeneous systems in \(\mathbb{R}^3\). The global behavior of this kind of systems are closely related to planar quadratic systems. Some new results are obtained by using the method of qualitative analysis.

MSC:

34C07 Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert’s 16th problem and ramifications) for ordinary differential equations
37E35 Flows on surfaces
34C37 Homoclinic and heteroclinic solutions to ordinary differential equations
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