On a partial integral which can be derived from poisson matrix |
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Authors: | D B Zotev |
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Institution: | (1) Department of Mathematics Applications, Volgograd State Technical University, Lenina ul. 28, 400131 Volgograd, Russia |
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Abstract: | Consider a surface which is a common level of some functions. Suppose that this surface is invariant under a Hamiltonian system.
The question is if a partial integral can be derived explicitly from the Poisson matrix of these functions. In some cases
such an integral is equal to the determinant of the matrix. This paper establishes a necessary and sufficient condition for
this to hold true. The partial integral that results is not trivial if the induced Poisson structure is non-degenerate at
one point at least. Therefore, the invariant surface must be even-dimensional. |
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Keywords: | 37J05 37J15 70S05 70H05 |
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