Period function and normalizers of vector fields in with n−1 first integrals

We extend the theory that relates period function, normalizers and first integrals, which has been widely developed in , to any dimension. In particular, we show how to find n−1 independent normalizers of vector fields in with n−1 independent first integrals. A formula for the derivatives of the period function is obtained and a necessary and sufficient condition for isochronicity is also proved. These results generalize previous works of Freire, Gasull and Guillamon, Sabatini and Villarini.