Hans Koch and Sasa Kocic Renormalization of Vector Fields and Diophantine Invariant Tori (116K, plain TeX) ABSTRACT. We extend the renormalization group techniques that were developed originally for Hamiltonian flows to more general vector fields on $\torus^d\times\real^\ell$. Each Diophantine vector $\omega\in\real^d$ determines an analytic manifold $W$ of infinitely renormalizable vector fields, and each vector field on $W$ is shown to have an elliptic invariant $d$-torus with frequencies $\omega_1,\omega_2,\ldots,\omega_d$. Analogous manifolds for particular classes of vector fields (Hamiltonian, divergence-free, symmetric, reversible) are obtained simply by restricting $\WW$ to the corresponding subspace. We also discuss nondegeneracy conditions, and the resulting reduction in the number of parameters needed in parametrized families to guarantee the existence of invariant tori.