Polynomial Differential Systems in R3 Having Invariant Weighted Homogeneous Surfaces
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2018-03-01
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In this paper we give the normal form of all polynomial differential systems in R3 having a weighted homogeneous surface f= 0 as an invariant algebraic surface and characterize among these systems those having a Darboux invariant constructed uniquely using this invariant surface. Using the obtained results we give some examples of stratified vector fields, when f= 0 is a singular surface. We also apply the obtained results to study the Vallis system, which is related to the so-called El Niño atmospheric phenomenon, when it has a cone as an invariant algebraic surface, performing a dynamical analysis of the flow of this system restricted to the invariant cone and providing a stratification for this singular surface.
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Bulletin of the Brazilian Mathematical Society, v. 49, n. 1, p. 137-157, 2018.