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2013
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# Sergey Ziglin

Mohovaya st., 11, Moscow, 125009 Russia
Institute of Radio-Engineering and Electronics of RAS

## Publications:

 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, no. 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. Keywords: Riemann problem, liquid ellipsoid, meromorphic first Citation: Ziglin S. L.,  On the absence of an additional meromorphic first integral in the Riemann problem on the motion of a homogeneous liquid ellipsoid, Regular and Chaotic Dynamics, 2010, vol. 15, no. 4-5, pp. 630-633 DOI:10.1134/S1560354710040155
 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. Citation: Ziglin S. L.,  On the Nonintegrability of a Dynamical System of the General Relativity, Regular and Chaotic Dynamics, 2000, vol. 5, no. 2, pp. 225-226 DOI:10.1070/RD2000v005n02ABEH000145
 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. Citation: 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, Regular and Chaotic Dynamics, 1997, vol. 2, nos. 3-4, pp. 124-125 DOI:10.1070/RD1997v002n04ABEH000052