The problem of the center for quartic differential systems with an affine invariant straight line and the line at infinity of maximal multiplicity

Olga Vacaraș, Dumitru Cozma

Abstract


Quartic differential systems with a center-focus critical point and non-degenerate infinity which admit an affine invariant straight line are studied. It is shown that, in this class, the maximal multiplicity of the line at infinity is six. Modulo the affine transformations and time rescaling the subclasses of systems with the line at infinity of multiplicity two, three,..., six are determined. Moreover, for quartic differential systems with an affine invariant straight line and the line at infinity of maximal multiplicity, the problem of the center is solved.


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References


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DOI: https://doi.org/10.52846/ami.v52i2.2270