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- W2952215865 abstract "In this paper we first give the explicit definition of essential perturbation. Secondly, given a perturbation of a particular family of centers of polynomial differential systems of arbitrary degree for which we explicitly know its Poincar'e--Liapunov constants, we give the structure of its $k$-th Melnikov function. This result generalizes the result obtained by Chicone and Jacobs for perturbations of degree at most two of any center of a quadratic polynomial system. Moreover we study the essential perturbations for all the centers of the differential systems [ dot{x} , = , -y + P_{rm d}(x,y), quad dot{y} , = , x + Q_{rm d}(x,y), ] where $P_{rm d}$ and $Q_{rm d}$ are homogeneous polynomials of degree ${rm d}$, for ${rm d}=2$ and ${rm d}=3$." @default.
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- W2952215865 date "2014-06-30" @default.
- W2952215865 modified "2023-10-17" @default.
- W2952215865 title "Essential perturbations of polynomial vector fields with a period annulus" @default.
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