THE HAMILTONIAN STRUCTURES OF 3D ODE WITH TIME-INDEPENDENT INVARIANTS

Applied Mathematics and Mechanics (English Edition) ›› 1995, Vol. 16 ›› Issue (4): 301-306.

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THE HAMILTONIAN STRUCTURES OF 3D ODE WITH TIME-INDEPENDENT INVARIANTS

郭仲衡¹, 陈玉明²

1. Department of Mathematics, Peking University, Beijig 100871, P. R. China;
2. Department of Applied Mathematics, Hunan University, Changsha 410012, P. R. China

收稿日期:1994-04-01 出版日期:1995-04-18 发布日期:1995-04-18

THE HAMILTONIAN STRUCTURES OF 3D ODE WITH TIME-INDEPENDENT INVARIANTS

Guo Zhong-heng¹, Chen Yu-ming²

1. Department of Mathematics, Peking University, Beijig 100871, P. R. China;
2. Department of Applied Mathematics, Hunan University, Changsha 410012, P. R. China

Received:1994-04-01 Online:1995-04-18 Published:1995-04-18

摘要/Abstract

摘要： We have proved that any 3-dimensional dynamical system of ordinary differentialequations(in short, 3D ODE)With time-independent invariants can be rewritten as Haniltonian systems with respect to generalized Poisson brackets and theHamiltonians are these invariants. As an example,we discuss the Kermack-Mckendrick modelfor epidemics in detail. The results we obtained are generalizatioof those obtained by Y. Nutku.

关键词: Poisson bracket, Hamiltonian structure, bi-Hamiltonianstructure, invariant, the Kermack-Mckendrick model for epidemics

Abstract: We have proved that any 3-dimensional dynamical system of ordinary differentialequations(in short, 3D ODE)With time-independent invariants can be rewritten as Haniltonian systems with respect to generalized Poisson brackets and theHamiltonians are these invariants. As an example,we discuss the Kermack-Mckendrick modelfor epidemics in detail. The results we obtained are generalizatioof those obtained by Y. Nutku.

Key words: Poisson bracket, Hamiltonian structure, bi-Hamiltonianstructure, invariant, the Kermack-Mckendrick model for epidemics

郭仲衡;陈玉明. THE HAMILTONIAN STRUCTURES OF 3D ODE WITH TIME-INDEPENDENT INVARIANTS[J]. Applied Mathematics and Mechanics (English Edition), 1995, 16(4): 301-306.

Guo Zhong-heng;Chen Yu-ming. THE HAMILTONIAN STRUCTURES OF 3D ODE WITH TIME-INDEPENDENT INVARIANTS[J]. Applied Mathematics and Mechanics (English Edition), 1995, 16(4): 301-306.

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THE HAMILTONIAN STRUCTURES OF 3D ODE WITH TIME-INDEPENDENT INVARIANTS

THE HAMILTONIAN STRUCTURES OF 3D ODE WITH TIME-INDEPENDENT INVARIANTS

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