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On the 60th birthday of V.I.Arnold
The linear variant of the Kozlov's theorem on the absence of first integrals being polinomial of a natural mechanical system in the case of branching of solutions
S. L. Ziglin 103907, Moscow, st. Mokhovaya, 11, Russia,
Institute of Radio Engineering and Electronics
Russian Academy of Sciences
Abstract:
We obtained the upper limit for the number of functionally independent rational first integrals for a subgroup of the group of affine transformations of a complex affine space of finite dimension. This value does not exceed the difference between the power of the maximal set of functionally independent rational first integrals for the corresponding linear group and the maximal rank of the system consisted of the differentials of these first integrals restricted to the subspace generated by those elements of this subgroup that represent shifts.
Received: 12.11.1997
Citation:
S. L. Ziglin, “The linear variant of the Kozlov's theorem on the absence of first integrals being polinomial of a natural mechanical system in the case of branching of solutions”, Regul. Chaotic Dyn., 2:3-4 (1997), 124–125
Linking options:
https://www.mathnet.ru/eng/rcd1014 https://www.mathnet.ru/eng/rcd/v2/i3/p124
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