Alexander Batkhin talk on the Computer Algebra Conference, June 26-28, 2023

For elementary singular point of a multiparameter Hamiltonian system we discuss a method of computing the condition of existence of a resonance of arbitrary order and multiplicity. For a certain resonant vector this condition defines a resonant variety as a variety in the space of coefficients of the characteristic polynomial of the linear part of the Hamiltonian system. By means of computer algebra and power geometry techniques polynomial parametrization of the resonant variety is proven. The obtained results can be used to investigate the formal stability regions of the equilibrium of a Hamiltonian multiparameter system as well as for the asymptotic integration of its normal form.