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Math"],"published-print":{"date-parts":[[2011,8]]},"abstract":"<jats:p>We go back to the results of Poincar\u00e9 [Poincare, H (1891) Sur lintegration des equations differentielles du premier ordre et du premier degre I and II,<jats:italic>Rendiconti del circolo matematico di Palermo<\/jats:italic><jats:bold>5<\/jats:bold>, 161\u2013191] on the multipliers of a periodic orbit for proving the<jats:italic>C<\/jats:italic><jats:sup>1<\/jats:sup>non-integrability of differential systems. 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