Global nilpotent reversible centers with cubic nonlinearities symmetric with respect to the y-axis

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2024年5月10日

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Montserrat Corbera,
Claudia Valls

摘要

We classify when the polynomial differential systems of the form $\dot{x} = y+ P_3(x,y)$ $\dot{x} = y + P_{3} (x, y)$ , $\dot{y} =Q_3(x,y)$ $\dot{y} = Q_{3} (x, y)$ , that are invariant under the change $(x,y,t)\mapsto (-x,y,-t)$ $(x, y, t) \mapsto (- x, y, - t)$ (here $P_3$ $P_{3}$ and $Q_3$ $Q_{3}$ are general polynomials of degree three) have global centers.