Limit cycles for a variant of a generalized Riccati equation
Copyright policy )Limit cycles for a variant of a generalized Riccati equation
Agraïments: The second author is partially supported by FCT/Portugal through UID/MAT/04459/2013 In this paper we provide a lower bound for the maximum number of limit cycles surrounding the origin of systems (x, y = x) given by a variant of the generalized Riccati equation \[ x x^2n 1 x b x^4n 3=0, \] where b>0, b \R, n is a non--negative integer and is a small parameter. The tool for proving this result uses Abelian integrals.
- Instituto Superior de Espinho Portugal
- University of Lisbon Portugal
- Technical University of Lisbon Portugal
- Autonomous University of Barcelona Spain
Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.), limit cycles, Abelian integrals, Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations, Nonlinear ordinary differential equations and systems, Perturbations, asymptotics of solutions to ordinary differential equations, Limit cycles, Generalized Riccati system, Weak 16th Hilbert problem, weak 16th Hilbert problem, abelian integral, generalized Riccati system
Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.), limit cycles, Abelian integrals, Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations, Nonlinear ordinary differential equations and systems, Perturbations, asymptotics of solutions to ordinary differential equations, Limit cycles, Generalized Riccati system, Weak 16th Hilbert problem, weak 16th Hilbert problem, abelian integral, generalized Riccati system
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