Periodic orbits for real planar polynomial vector fields of degree \(n\) having \(n\) invariant straight lines taking into account their multiplicities. (English) Zbl 1349.34142
Summary: We study the existence and non-existence of periodic orbits and limit cycles for planar polynomial differential systems of degree \(n\) having \(n\) real invariant straight lines taking into account their multiplicities. The polynomial differential systems with \(n=1,2,3\) are completely characterized.
MSC:
| 34C45 | Invariant manifolds for ordinary differential equations |
| 34C05 | Topological structure of integral curves, singular points, limit cycles of ordinary differential equations |
| 34A34 | Nonlinear ordinary differential equations and systems |
| 34C14 | Symmetries, invariants of ordinary differential equations |
