Normal forms of implicit differential equations and Liouville fields (Q1356299)

The author presents normal forms, which are the germs of Liouville fields of the type \(S+N\), where \(S\) is a semisimple linear Liouville field and \(N\) is a germ of a Hamiltonian field commuting with \(S\), where \(N^1\) is nilpotent. The author shows that in dimension 2, every hyperbolic germ of a Liouville field is conjugate to a polynomial normal form. The advantages of a polynomial normal form based on the fact that its coefficients are the invariants of conjugation.