Hamiltonian vector fields of homogeneous polynomials in two variables

الأصل · EN

Let g:R² be a homogeneous polynomial of degree p>1, G=(-g'y, g'ₓ) be its Hamiltonian vector field, and Gₜ be the local flow generated by G. Denote by E(G,O) the space of germs of C∞ diffeomorphisms (R²,O)→(R²,O) that preserve orbits of G. Let also Eid(G,O) be the identity component of E(G,O) with respect to C¹-topology. Suppose that g has no multiple prime factors. Then we prove that for every h∈ Eid(G,O) there exists a germ of a smooth function α:R² at O such that h(z)=Gα₍z₎(z).