Scalar autonomous second order ordinary differential equations

• Autores: Clodoaldo Grotta Ragazzo
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 11, Nº 2, 2012, págs. 277-415
• Idioma: inglés
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• Resumen

  • 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) .