REVIEW ON THE RESEARCHES OFGENERALIZED HAMILTONIAN SYSTEMS
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摘要:用广义Ｐｏｉｓｓｏｎ括号直接定义的广义Ｈａｍｉｌｔｏｎ系统是经典Ｈａｍｉｌｔｏｎ系统的一种推广。由于它的维数没有限制，同时它又保持了经典Ｈａｍｉｌｔｏｎ系统的主要性质，因此具有更大的普遍性和广泛的应用前景。本文简要介绍了广义Ｈａｍｉｌｔｏｎ系统理论的发展历史、基本概念和研究现状。Abstract:The generalized Hamiltonian system (GHS), defined directly by thegeneralized Poisson bracket, is a generalization of the traditional Hamiltoniansystem defined on (even dim.) symplectic manifold. The GHS can describe moregeneral dynamical systems including odd- and ∞-dimensional systems, hence thestudy on this type of systems will bc very important in theory and applications.In this paper, we give a review on the researches of generalized Hamiltoniansystems in China and abroad.
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