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Integrability of two dimensional quasi-homogeneous polynomial differential systems. (English) Zbl 1213.37093
The authors deal with polynomial differential systems $$ (\dot{x},\dot{y})^{T}=F_{r}=(P,Q)^{T}, \tag1$$ where $F_{r}$ is a quasi-homogeneous polynomial vector field of degree $r\in N \cup {0}$ with respect to type $t=(t_{1},t_{2})\in N^{2},$ i.e., for any arbitrary positive real $\varepsilon$, $P(\varepsilon^{t_{1}}x,\varepsilon^{t_{2}}y)= \varepsilon^{r+t_{1}}P(x,y)$, $Q(\varepsilon^{t_{1}}x,\varepsilon^{t_{2}}y)= \varepsilon^{r+t_{2}}Q(x,y)$ and interested in analyzing when system (1) is analytically integrable.

MSC:
37K05Hamiltonian structures, symmetries, variational principles, conservation laws
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References:
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