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 Volume 1, Number 1, 2011, Pages 33-52                                                                DOI：10.11948/2011004 On the integrability of the differential systems in dimension two and of the polynomial differential systems in arbitrary dimension Jaume Llibre Keywords: Abstract: This is a survey on recent results providing sufficient conditions for the existence of a first integral, first for vector fields defined on real surfaces, and second for polynomial vector fields in $R^n$ or $C^n$ with $n\geq 2$. We also provide an open question and some applications based on the existence of such first integrals. PDF      Download reader