具有不依赖于时间的不变量的三维常微分方程组的Hamilton结构

The Hamiltonian Structures of 3D ODE with Time-Independent Invariants

本文证明了具有不依赖于时间的不变量的三维常微分方程组所描述的动力系统相对于一广义Ｐｏｉｓｓｏｎ括号可以改写为Ｈａｍｉｌｔｏｎ系统，并且这些不变量就是Ｈａｍｉｌｔｏｎ量。作为例子，我们讨论了Ｋｅｒｍａｃｋ－Ｍｃｋｅｎｄｒｉｃｋ传染病模型，所得结果推广了Ｙ．Ｎｕｔｋｕ的结果。

We have proved that any 3-dimensional dynamical system of ordinary differ-ential equations(in short,3D ODE) with time-independent invariants can be rewritten as Hamiltonian systems with respect to generalized Poisson brackets and the Hamiltonians are these invariants.As an example,we discuss the Ker-mack-Mckendricd model for epidemics in detail.The results we obtained are generalization of those obtained by Y. Nutku.