Real forms of the complex Neumann system: A method for finding real roots of polynomial U-s (lambda)

摘要

The 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 U-s (lambda). For certain polynomials, the existence and positions of the real roots, according to the suitable parameters of the system, is not obvious.