| 马文秀.一些多项式型的有限维对合系[J].数学研究及应用,1990,10(4):509~515 |
| 一些多项式型的有限维对合系 |
| Some Finite-Dimensional Involutive Systems with Polynomial Forms |
| 投稿时间：1989-09-08 |
| DOI：10.3770/j.issn:1000-341X.1990.04.007 |
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| In this paper, starting from the combination of two in volutive systems, we consider separately some systems of polynomial functions:{Im(1)=Bm Rm}m=0∞, {Im(2)=Bm Sm}m=0∞, {Im(3)=Bm Tm}m=0∞ and so on; and analyse carefully the sufft cient and necessary conditions of the involution of three systems of functions {Im(i)}m=0∞(1≤i≤3) with general coefficients.Furthermore,we present concrete forms of the involutive systems hidden in {Im(i)}m=0∞(1≤i≤3);and thus obtain six kinds of nontrivial involutive systems of functions, which include a few involutive systems discussed inthe literature. Based upon these involutive systems, we can generate a lot of new finite-dimensional Hamiltonian systems which are completely integrable in the sense of Liouville. |
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