Algebraic limit cycles for quadratic polynomial differential systems
Copyright policy )Algebraic limit cycles for quadratic polynomial differential systems
AbstractAlgebraic limit cycles in quadratic polynomial differential systems started to be studied in 1958, and a few years later the following conjecture appeared: quadratic polynomial differential systems have at most one algebraic limit cycle. We prove that a quadratic polynomial differential system having an invariant algebraic curve with at most one pair of diametrically opposite singular points at infinity has at most one algebraic limit cycle. Our result provides a partial positive answer to this conjecture.
- University of Lisbon Portugal
- Instituto Superior de Espinho Portugal
- Autonomous University of Barcelona Spain
quadratic polynomial differential system, Quadratic polynomial vector field, Algebraic limit cycles, Quadratic polynomial differential system, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, quadratic polynomial vector field, Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations, Hilbert's 16th problem, algebraic limit cycle
quadratic polynomial differential system, Quadratic polynomial vector field, Algebraic limit cycles, Quadratic polynomial differential system, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, quadratic polynomial vector field, Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations, Hilbert's 16th problem, algebraic limit cycle
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