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Poincaré’s reversibility condition. (English) Zbl 1004.34015

Consider a real planar analytic vector field where the origin is a center for the linearization of the planar field. The Poincaré reversibility condition says that if the system is reversible with respect to a line which passes through the origin, then the origin is a center. The author gives necessary and sufficient conditions for the existence of a reversibility line for any analytic system. Quadratic and cubic systems as well as non-Hamiltonian systems are studied.

MSC:

34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
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