On new directions of Group Analysis of ordinary Differential Equations

V.F.Zaitsev

Russian State Pedagogical University

Moyka, 48, 191186, Saint-Petersburg, Russia

zaitsev@osipenko.stu.neva.ru

In this paper we elucidated the activity of the Saint-Petersburg school of group analysis of ordinary differential equations for the last decade. This step was preceded by creation of bases of the theory and the techniques of an application of discrete group analysis. We consider the problem of maximality of admissible discrete transformation groups, theory of formal operators, factorization theorems, the generalized Ermakov equation and examples.