Resumen de Scalar autonomous second order ordinary differential equations

Clodoaldo Grotta Ragazzo

• This paper is about equations of the form u˙=v,v˙=F(u,v)where(u,v)∈R2 and F is an infinitely differentiable function. Its main theorem states that if F(u, −v) = F(u, v) then, under some additional conditions, there exists an infinitely differentiable change of variables (u, v) → (x, y) onto R2 such that in the new variables the equation becomes x˙=y,y˙=g(x) .