Psi-series, singularities of solutions and integrability of polynomial systems
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Psi-series (i.e., logarithmic series) of $m$-dimensional polynomial systems are considered. Its existence and convergence is studied, and an algorithm of location of logarithmic singularities is developed. Moreover, the relationship between psi-series and non-integrability is stressed and in particular it is stated that $m$-dimensional polynomial systems with psi-series which do not reduce to Laurent series do not have $m-1$ independent algebraic first integrals.