Sergey Ziglin
Mohovaya st., 11, Moscow, 125009 Russia
Institute of Radio-Engineering and Electronics of RAS
Publications:
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Ziglin S. L.
On the absence of an additional meromorphic first integral in the Riemann problem on the motion of a homogeneous liquid ellipsoid
2010, vol. 15, nos. 4-5, pp. 630-633
Abstract
We prove the absence of an additional meromorphic first integral in the Riemann problem on the motion of a homogeneous liquid ellipsoid with zero angular and vortex momenta in the case of zero self-gravitation.
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Ziglin S. L.
On the Nonintegrability of a Dynamical System of the General Relativity
2000, vol. 5, no. 2, pp. 225-226
Abstract
The absence of an additional meromorphic first integral of a Hamiltonian system with two degrees of freedom emerging in describing of the Friedman cosmological models with the coupled scalar field is proved.
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Ziglin S. L.
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
1997, vol. 2, nos. 3-4, pp. 124-125
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.
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