The first derivative of the period function of a plane vector field (Q1365658)

An algorithm to compute the derivatives of the Poincaré return map introduced in [\textit{J.-P. Françoise}, Ergodic Theory Dyn. Syst. 16, No. 1, 87-96 (1996; Zbl 0852.34008)] is used to compute the first nonzero derivative of the period function. The algorithm is somewhat different from traditional power series methods in that it uses a nontrivial application of the calculus of differential forms. Especially, a new result on the decomposition of 1-forms is derived.