Differential Resultant, Computer Algebra and Completely Integrable Dynamical Systems

摘要

For a pair of differential operators A and B with periodic coefficients we construct their differential resultant and derive condition for their commutativity. By considering this condition as a stationary Lax representation we are able to treat completely integrable dynamical systems. As special cases we obtain Henon-Heiles dynamical systems. We propose algorithms to do this by using the powerful methods of computer algebra and performing symbolic calculations in Maple 13 and Reduce4.