Abstract

I will present some results about orbital normal forms for vector fields $x\prime =y+...,\; y\prime =...,$ which were obtained with E. Strozyna. Firstly, we obtained complete formal normal forms. Secondly, we showed that the Takens preliminary form $x\prime =y+a(x),\; y\prime =b(x),$ can be chosen analytic, if the initial system is analytic.