Davydenko A. Investigation of the Behaviour of the Solutionns of the Nonlinear System of Differential Equations in the Neighbourhood of Their Invariant Toroidal Manifolds

Українська версія

Thesis for the degree of Candidate of Sciences (CSc)

State registration number

0403U000877

Thesis Registration Form

0403U000877.pdf

Applicant for

Specialization

  • 01.01.02 - Диференційні рівняння

11-03-2003

Specialized Academic Board

Д 26.206.02

The Institute of Mathematics of NASU

Essay

There have been considered the problem of complementability of the system of periodic vector-functions to periodic basis, where the new conditions of complementability are to be found. The obtained results have been applied for introduction of local coordinates in a small neighbourhood of invariant toroidal manifold of an autonomous system of the differential equations. There have been found some useful properties of obtained systems of the differential equations in local coordinates and their linearizations - linear expansions of the dynamic systems on a torus.

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