Poincaré and Poincaré-Cartan integral invariants of a generalized Hamiltonian system

Abstract

Without Darboux's transformation, the traditional Hamiltonian formulation of dynamical systems is only suitable to conservative systems or self-adjoint systems. Based on an extension of dynamic space of Birkhoffian systems to a generalized phase space by introducing dummy variables, a generalized Hamiltonian canonical formulation of general systems is constructed, which admits symplectic structure. There exist integral invariants of Poincaré and Poincaré-Cartan's type for such systems.