Global Nilpotent Reversible Centers with Cubic Nonlinearities Symmetric with Respect to the x-Axis

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2024年4月13日

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Montserrat Corbera,
Claudia Valls

摘要

Let $P_3(x,y)$ $P_{3} (x, y)$ and $Q_3(x,y)$ $Q_{3} (x, y)$ be polynomials of degree three without constant or linear terms. We characterize the global centers of all 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 reversible and invariant with respect to the x-axis.