Phase portraits of reversible linear differential systems with cubic homogeneous polynomial nonlinearities having a non-degenerate center at the origin. (English) Zbl 1311.34061
Summary: We classify the global phase portraits of all reversible linear differential systems with cubic homogeneous polynomial nonlinearities defined in the plane and having a non degenerate center at the origin. The reversibility is given by a linear involution having a fixed set of dimension 1.
MSC:
| 34C05 | Topological structure of integral curves, singular points, limit cycles of ordinary differential equations |
| 34C14 | Symmetries, invariants of ordinary differential equations |
| 34C07 | Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert’s 16th problem and ramifications) for ordinary differential equations |
