Phase portraits of the complex Abel polynomial differential systems. (English) Zbl 1485.34099
Summary: In this paper we characterize the phase portraits of the complex Abel polynomial differential equations
\[
\dot{z}=(z-a)(z-b)(z-c),
\]
with \(z\in\mathbb{C}\), \(a,b,c\in\mathbb{C}\). We give the complete description of their topological phase portraits in the Poincaré disc, i.e. in the compactification of \(\mathbb{R}^2\) adding the circle \(\mathbb{S}^1\) of the infinity.
MSC:
| 34C05 | Topological structure of integral curves, singular points, limit cycles of ordinary differential equations |
| 34A05 | Explicit solutions, first integrals of ordinary differential equations |
| 37C10 | Dynamics induced by flows and semiflows |
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