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1:-3 resonant centers on 2 with homogeneous cubic nonlinearities. (English) Zbl 1165.34334
Summary: We characterize the collection of systems of differential equations on 2 of the form x ' =x+p(x,y), y ' =-3y+q(x,y), where p and q are homogeneous polynomials of degree three (either of which may be zero), that possess a first integral in a neighborhood of (0,0) of the form x 3 y+, where omitted terms are of order at least five. Such systems are called 1:-3 resonant centers.
34C05Location of integral curves, singular points, limit cycles (ODE)
34C20Transformation and reduction of ODE and systems, normal forms
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