Resumen de First derivative of the period function with applications

Emilio Freire Macías , Armengol Gasull i Embid , Antoni Guillamon Grabolosa

• In the present paper, inspired in the geometrical ideas involved in the Lie bracket, we give a method to prove that some centres have either an increasing or a decreasing period function. This method is based on a formula for computing the derivative of the period function, which is obtained from the knowledge of the set of normalizers of the centre. The following Theorem is the main result of our work.