Adiabatic invariants of slowly varying three-dimensional systems and existence of invariant tori of Lotka-Volterra equation

作者：Li J^*; Zhao X; Liu Z

来源：Acta Mathematicae Applicatae Sinica-English Series, 1996, 12(2): 201-208.

• Adiabatic invariant
• Hamiltonian structure
• Lotka-Volterra equation
• Slowly varying systems

In this paper, we use the theory of generalized Poisson bracket (GPB) to build the Poisson structure of three-dimensional "frozen" systems of Hamiltonian systems with slow time variable, and show that under proper conditions, there exists an adiabatic invariant on every closed simply connected symplectic leaf for the time-dependent Hamiltonian systems. If the Hamiltonian H(p,q,τ) on these symplectic leaves are periodic with respect to T and the frozen systems are in some sense strictly nonisochronous, then there are perpetual adiabatic invariants. To illustrate these results, we discuss the classical Lotka-Volterra equation with slowly periodic time-dependent coefficients modeling the interactions of three species.

• 出版日期1996
• 单位云南大学