Аннотация:
In this paper we provide affine invariant necessary and sufficient conditions for a non-degenerate quadratic differential system to have an invariant conic $f(x, y)=0$ and a Darboux invariant of the form $f(x, y)^\lambda e^{st}$ with $\lambda,s\in \mathbb{R}$ and $s\ne0$. The family of all such systems has a total of seven topologically distinct phase portraits. For each one of these seven phase portraits we provide necessary and sufficient conditions in terms of affine invariant polynomials for a non-degenerate quadratic system in this family to possess this phase portrait.
Ключевые слова и фразы:
quadratic differential system, invariant conic, darboux invariant, affine invariant polynomial, group action, phase portrait.
Полный текст:
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