Speciality:
01.04.07 (Physics of condensed states)
E-mail: ,
Keywords: integrable Hamiltonian systems; celestial mechanics in spaces of constant curvatute; topology; topological invariants, bifurcation analysis, symmetries; application of Lie groups to integrable systems.
Subject:
First works are connected with theoretical study of the diffusion in metals and alloys. Properties of the diffusion under different boundary and external conditions were studied: at irradiation by protons; under the conditions of temperature gradient (cycling); in the field of external tensions, in metals and construction steels. The microscopic model of calculation of the heat of transport due to lattice expansion is constructed. The model of diffusion in amorphous alloy metal–metalloid in the field of external tensions (the results of theoretical calculation satisfy the experiment). At the present time scientific interests connected with integrable Hamiltonian systems, in particular, with dynamical systems in celestial mechanics in cpaces of constant curvature. The generalized problem of two centers (the motion of a material point in the field generated by two fixed centers) on the 3-sphere was studied. The bifurcation set in the plane of integrals of motion was constructed and the classification of the domains of possible motion was carried out. All kinds of motion (regular motions and limit motions corresponding to bifurcations of Liouville tori) on the configurational space are described. The topological analysis of this problem (with A.A. Oshemkov) was carried out. The Fomenko–Zieschang invariants, which completely describe the topology of Liouville foliations of isoenergy 3-manifolds $Q^3$, are constructed. The regularization of the Kepler problem on a sphere was carried out. The generalization of some problems of celestial mechanics to the space of Lobachevsky was stadied: the two-center problem, Lagrange's problem (when one of the centers is removed at infinity) was studied. The integrability was proved, the bifurcation set was obtained, the classification of the domains of possible motion was carried out. The bifurcation analysis of the problem of the Kovalevskaya top at the change of Kolosov is carried out (the top motion is reduced to the motion of a mass point).
Main publications:
Vozmischeva T. G. Mathematical aspects in the celestial mechanics: the Lobachevsky space. International Conference "Geometry, Integrability and Quantization", Bulgaria, 2000, Proceedings.
Vozmischeva T. G. Bifurcations of first integrals in the case of Kovalevskaya at the change of Kolosov. International Conference "Geometrization of Physics IV" 4–8 October 1999, Kazan State University, Proceedings.
Vozmischeva T. G. Classification of motions for generalization of the two-center problem on a sphere // Cel. Mech. and Dyn. Astr., 2000, 77, 37–48.
Vozmischeva T. G. Some integrable problems in celestial mechanics in spaces of constant curvature. Contemporary mathematics and its application // Thematic surveys. Dinamicheskie systemy-12, 2002, v. 88 (published).
