On the centers of cubic polynomial differential systems with four invariant straight lines
Copyright policy )On the centers of cubic polynomial differential systems with four invariant straight lines
Assume that a cubic polynomial differential system in the plane has four invariant straight lines in generic position, i.e. they are not parallel and no more than two straight lines intersect in a point. Then such a differential system only can have 0, 1 or 3 centers.
Cubic system, Cubic polynomial differential systems, center, Centers, cubic polynomial differential systems, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, Invariant straight line, Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations, Invariant manifolds for ordinary differential equations, invariant straight line
Cubic system, Cubic polynomial differential systems, center, Centers, cubic polynomial differential systems, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, Invariant straight line, Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations, Invariant manifolds for ordinary differential equations, invariant straight line
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