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- W2952587849 abstract "Let X be a homogeneous polynomial vector field of degree 2 on S^2. We show that if X has at least a non--hyperbolic singularity, then it has no limit cycles. We give necessary and sufficient conditions for determining if a singularity of X on S^2 is a center and we characterize the global phase portrait of X modulo limit cycles. We also study the Hopf bifurcation of X and we reduce the 16^{th} Hilbert's problem restricted to this class of polynomial vector fields to the study of two particular families. Moreover, we present two criteria for studying the nonexistence of periodic orbits for homogeneous polynomial vector fields on S^2 of degree n." @default.
- W2952587849 created "2019-06-27" @default.
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- W2952587849 date "2008-10-15" @default.
- W2952587849 modified "2023-09-27" @default.
- W2952587849 title "Phase portraits for quadratic homogeneous polynomial vector fields on S^2" @default.
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