Русская версия
ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

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Calculation of the Invariant Decomposition of the Tangent Space

Author(s):

Georgii Sergeevich Osipenko

Doctor of Physical and Mathematical Sciences, Full Professor of the Moscow State University named by M.V. Lomonosov, Full Professor of the Department of Computational Mathematics in the Sevastopol Branch of MGU

george.osipenko@mail.ru

Irina Alexeevna Andreeva

Candidate of Physical and Mathematical Sciences, Docent of the Higher Mathematics Department in the Peter the Great St.Petersburg Polytechnic University (SPbPU)

irandr@inbox.ru

Abstract:

A discrete dynamic system generated by a diffeomorphism is considered. The task of constructing an invariant decomposition of the tangent space is set. This task is reduced to calculating the components of a chain recurrent set on a projective bundle. A computer-oriented tool for such a calculation is a symbolic image of a dynamic system, which is an oriented graph. The components of the chain recurrent set are determined by calculating the components of the strong connectivity of the symbolic image. A nontrivial example of calculating the desired tangent space decomposition is given.

Keywords

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