2019
Том 71
№ 11

All Issues

Fil' B. N.

Articles: 3
Article (Ukrainian)

Category of topological jet manifolds and certain applications in the theory of nonlinear infinite-dimensional dynamical systems

Fil' B. N., Prykarpatsky A. K.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1992. - 44, № 9. - pp. 1242–1256

A new category of topological jet manifolds is proposed for the purpose of investigating exact finite-dimensional approximations of nonlinear dynamical systems on infinite-dimensional functional manifolds. Differential geometry structures on these manifolds and their applications to the theory of integrability in quadratures of nonlinear dynamical Lax-type systems are studied.

Article (Ukrainian)

Some aspects of a gradient holonomic algorithm in the theory of integrability of nonlinear dynamic systems and computer algebra problems

Fil' B. N., Mitropolskiy Yu. A., Prykarpatsky A. K.

Full text (.pdf)

Ukr. Mat. Zh. - 1991. - 43, № 1. - pp. 78-81

Article (Ukrainian)

Quantum lie algebra of currents ? The universal algebraic structure of symmetries of completely integrable dynamical systems

Fil' B. N., Pritula N. N., Prykarpatsky A. K.

Full text (.pdf)

Ukr. Mat. Zh. - 1988. - 40, № 6. - pp. 764–768