Ordinary differential equations described by their Lie symmetry algebra
  The theory of Lie remarkable equations, i.e. differential equations characterized by their Lie point symmetries, is reviewed and applied to ordinary differential equations. In particular, we consider some relevant Lie algebras of vector fields on $\mathbb{R}^k$ and characterize Lie remarkable equations admitted by the considered Lie algebras. 
Gianni Manno, Francesco Oliveri, Giuseppe Saccomandi, Raffaele Vitolo
math-ph math.DG math.MP