Structure of the resonance set of a real polynomial

Abstract:

We consider the resonance set of a real polynomial, i.e. the set of all the points of the coefficient space at which the polynomial has commensurable zeroes. The constructive algorithm of computation of polynomial representation of the resonance set is provided. The structure of the resonance set of a polynomial of degree n is described in terms of partitions of number n. The main algorithms, described in the preprint, are organized as a library of the computer algebra system Maple. The description of the resonance set of cubic is given. Obtained results are used for solving the problem of formal stability of a stationary point of a multiparametric Hamiltonian problem with three degrees of freedom.

Keywords:

elimination theory, subresultant, computer algebra, formal stability of a stationary point

Publication language:russian, pages:23

Research direction:

Mathematical problems and theory of numerical methods