Real forms of the complex Neumann systemNovak, Tina (Avtor) Žerovnik, Janez (Avtor) roots of a polynomialcomplex Neumann systemArnold-Liouville level setspositive solutionsystem of linear equationsThe topology of Arnold-Liouville level sets of the real forms of the complex generic Neumann system depends indirectly on the positions of the roots of the special polynomial Us ([lambda]). For certain polynomials, the existence and positions of the real roots, according to the suitable parameters of the system, is not obvious. In the paper, a method for checking the existence and positions of the real roots of the polynomials Us ([lambda]) is given. The method and algorithm are based on searching of a positive solution of a system of linear equations. In case [eta]=2 , we provide a complete solution to the problem of existence of real roots for all special polynomials and determine the topology of the Arnold-Liouville level sets.20212022-01-18 13:13:34Članek v reviji134490sl