Automorphisms of ℂ^3 Commuting with a ℂ^+-Action

Let rho be an algebraic action of the additive group C^+ on the three-dimensional affine space C^3. We describe the group Cent(rho) of polynomial automorphisms of C^3 that commute with rho. A particular emphasis lies in the description of the automorphisms in Cent(rho) coming from algebraic C^+-actions. As an application, we prove that the automorphisms in Cent(rho) that are the identity on the algebraic quotient of rho form a characteristic subgroup of Cent(rho).