Normal Forms near Two-Dimensional Resonance Tori for the Multidimensional Anharmonic Oscillator

We study the problem of constructing a normal form near a two-dimensional invariant isotropic torus for a multidimensional anharmonic oscillator. We construct a fourth-order normal form with respect to harmonic oscillator type variables. We show that, in the presence of resonances, the dependence of the normal form on the action type variables becomes nonpolynomial.