The period function of reversible quadratic centers
نویسندگان
چکیده
منابع مشابه
The Cyclicity of Period Annuli of a Quadratic Reversible Lotka-Volterra System with Two Centers
This paper is concerned with the bifurcations of limit cycles in a quadratic reversible Lotka-Volterra system with two centers under quadratic perturbations. By studying the number of zeros of Abelian integral based on the geometric properties of some planar curves, we obtain the cyclicity of each periodic annulus of the system under quadratic perturbations is two, and the cyclicity of two peri...
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Very little is known about the period function for large families of centers. In one of the pioneering works on this problem, Chicone [?] conjectured that all the centers encountered in the family of second-order differential equations ẍ = V (x, ẋ), being V a quadratic polynomial, should have a monotone period function. Chicone solved some of the cases but some others remain still unsolved. In ...
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We study the stratum in the set of all quadratic differential systems ẋ = P2(x, y), ẏ = Q2(x, y) with a center, known as the codimension-four case Q4. It has a center and a node and a rational first integral. The limit cycles under small quadratic perturbations in the system are determined by the zeros of the first Poincaré-Pontryagin-Melnikov integral I. We show that the orbits of the unpertur...
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The cyclicity of period annuli of some classes of reversible and non-Hamiltonian quadratic systems under quadratic perturbations are studied. The argument principle method and the centroid curve method are combined to prove that the related Abelian integral has at most two zeros.
متن کاملBifurcation of limit cycles from a quadratic reversible center with the unbounded elliptic separatrix
The paper is concerned with the bifurcation of limit cycles in general quadratic perturbations of a quadratic reversible and non-Hamiltonian system, whose period annulus is bounded by an elliptic separatrix related to a singularity at infinity in the poincar'{e} disk. Attention goes to the number of limit cycles produced by the period annulus under perturbations. By using the appropriate Picard...
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ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 2006
ISSN: 0022-0396
DOI: 10.1016/j.jde.2005.07.024