Speciality:
01.01.04 (Geometry and topology)
Birth date:
13.03.1945
E-mail: ,
Website: http://dfgm.math.msu.su/people/fomenko/ Keywords: minimal surfaces,
Plateau problem,
topology and geometry of Lie groups,
homogeneous spaces,
dynamical systems,
integrable Hamiltonian equations,
topological invariants of dynamical systems,
computer geometry,
topology of three-dimensional manifolds,
Hamiltonian mechanics,
symplectic geometry.
Subject:
In the theory of minimal surfaces was proved the multidimensional Plateau problem in the class of spectral bordisms of Riemannian manifolds. Then, as application of this general construction, was proved the global minimality of many well-known submanifolds in homogeneous Riemannian spaces of compact Lie groups. New scientific branch was developed, namely, the theory of topological classification of nondegenerate Hamiltonian differential equations (dynamical systems) of general type. New topological invariants, describing the topological type of singularities of dynamical systems, were discovered. As a result, was obtained the classification of integrable Hamiltonian systems with two degrees of freedom, up to Liouville equivalence and up to orbital equivalence (of topological and smooth type).
Main publications:
Fomenko A. T., “Periodichnost Botta s tochki zreniya mnogomernogo funktsionala Dirikhle”, Izv. AN SSSR. Ser. matem., 35:3 (1971), 667–681
Fomenko A. T., “Mnogomernaya zadacha Plato v rimanovykh mnogoobraziyakh”, Matem. sb., 89:3 (1972), 475–519
Mischenko A. S., Fomenko A. T., “Obobschennyi metod Liuvillya integrirovaniya gamiltonovykh sistem”, Funkts. analiz i ego prilozh., 12:2 (1978), 46–56
Fomenko A. T., “Teoriya Morsa integriruemykh gamiltonovykh sistem”, Dokl. AN SSSR, 287:5 (1986), 1071–1075
