2019
Том 71
№ 6

All Issues

Bogolyubov N. N.

Articles: 6
Article (English)

Generalized de Rham-Hodge complexes, the related characteristic Chern classes, and some applications to integrable multidimensional differential systems on Riemannian manifolds

Bogolyubov N. N., Prykarpatsky A. K.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2007. - 59, № 3. - pp. 327–344

We study the differential-geometric aspects of generalized de Rham-Hodge complexes naturally related to integrable multidimensional differential systems of the M. Gromov type, as well as the geometric structure of the Chern characteristic classes. Special differential invariants of the Chern type are constructed, their importance for the integrability of multidimensional nonlinear differential systems on Riemannian manifolds is discussed. An example of the three-dimensional Davey-Stewartson-type nonlinear integrable differential system is considered, its Cartan type connection mapping, and related Chern-type differential invariants are analyzed.

Article (Ukrainian)

A bilocal periodic problem for the Sturm-Liouville and Dirac operators and some applications to the theory of nonlinear dynamical systems. I

Bogolyubov N. N., Prykarpatsky A. K.

Full text (.pdf)

Ukr. Mat. Zh. - 1990. - 42, № 6. - pp. 794–800

Article (Ukrainian)

Bogolyubov's functional equation and the lie-poisson-lasov simplectic structure associated with it

Bogolyubov N. N., Prykarpatsky A. K., Samoilenko V. G.

Full text (.pdf)

Ukr. Mat. Zh. - 1986. - 38, № 6. - pp. 774–778

Article (Ukrainian)

N. N. Bogolyubov's quantum method of generating functionals in statistical physics: The current Lie algebra, its representations, and functional equations

Bogolyubov N. N., Prykarpatsky A. K.

Full text (.pdf)

Ukr. Mat. Zh. - 1986. - 38, № 3. - pp. 284–289

Article (Russian)

Calculation of tree energy for model systems

Bogolyubov N. N.

Full text (.pdf)

Ukr. Mat. Zh. - 1965. - 17, № 3. - pp. 3-15

Article (Russian)

On periodic solutions of differential equations of the $n$-th order with a small parameter

Bogolyubov N. N., Sadovnikov B. I.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1961. - 13, № 3. - pp. 3-12

An asymptotic method of constructing periodic solutions is developed for differential equations of the $n$-th order containing a small parameter. The method makes use of expansions in integral powers of the small parameter. A method of investigating the stability of the resulting solutions is presented. The convergence of the expansions is proved.