Generating Function Methods for Coefficient-Varying Generalized Hamiltonian Systems (Advances in Applied Mathematics and Mechanics, 2014)
The generating function methods have been applied successfully togeneralized Hamiltonian systems with constant or invertiblePoisson-structure matrices. In this paper, we extend these resultsand present the generating function methods preserving the Poissonstructures for generalized Hamiltonian systems with generalvariable Poisson-structure matrices. In particular, some obtainedPoisson schemes are applied efficiently to some dynamical systemswhich can be written into generalized Hamiltonian systems (such asgeneralized Lotka-Volterra systems, Robbins equations and so on).