Mathematics

In this seminar I will discuss the so called Painlevé test for ODEs, which is a useful algorithm to figure out if an ODE or a system of ODEs is of P-type. In particular I will focus my attention on the so called $\alpha$-method introduced by Painlevé and on the test introduced by Kovalevsky and Gambier.  I will illustrate how the two algorithms work though several examples and I will use them in order to classify which ODE of the first order are of P-type and to prove that $P_I$ is of P-type.