On symplectic and multisymplectic structures and their discrete versions in Lagrangian formalism
On symplectic and multisymplectic structures and their discrete versions in Lagrangian formalism
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DOI：
10.1088/0253-6102/35/6/703
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发表时间：
2001-04
影响因子：
3.1
通讯作者：
Han-Ying Guo;Yu-qi Li;Ke Wu
中科院分区：
文献类型：
--
作者：
Han-Ying Guo;Yu-qi Li;Ke Wu
我们引入欧拉-拉格朗日上同调，分别研究有限维和无限维拉格朗日系统中的辛结构和多重辛结构及其守恒性质，并利用差值离散变分原理和正则格上的非交换微分学，探讨了它们在相关正则离散有限维和无限维拉格朗日系统中的某些差异离散对应物。为了表明在所有这些情况下辛和多辛保持性质不一定依赖于相关的欧拉-拉格朗日方程，采用了欧拉-拉格朗日上同调概念和配置空间中的内容。
We introduce the Euler-Lagrange cohomology to study the symplectic and multisymplectic structures and their preserving properties in finite and infinite dimensional Lagrangian systems respectively We also explore their cei tain difference discrete counterparts in the relevant regularly discretized finite and infinite dimensional Lagrangian systems by means of the difference discrete variational principle with the difference being regarded as an entire geometric object and the noncommutative differential calculus on regular lattice. In order to show that in all these cases the symplectic and multisymplectic preserving properties do not necessarily depend on the relevant Euler-Lagrange equations, the Euler-Lagrange cohomological concepts and content in the configuration space are employed.