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

About the Group Analysis of Holomorphic Discrete Dynamic Systems

Author(s):

Viktor Gorbuzov

Department of mathematical analysis,
differential equations and algebra,
Faculty of Mathematics and Information Science,
Yanka Kupala State University of Grodno,
Ozeshko str. 22, Grodno,
Republic of Belarus, 230023

gorbuzov@grsu.by

Valentine Yur'yevich Tyshchenko

Grodno state university,
Mathematics and computer science faculty

valentinet@mail.ru

Abstract:

We consider real holomorphic discrete dynamic systems generated by one biholomorphysm. For arbitrary absolute and relative invariants of discrete dynamic systems of a given class functional representations are received. The algorithm of construction of the whole set of holomorphic systems of Pfaffian equations (including completely integrated) admitting the given biholomorphism is described. In the paper the algorithm of construction of the whole set of holomorphic systems of autonomous equations in total differentials (including completely solvable) admitting the given biholomorphism is described. The construction of the whole set of local one-parameter Lie groups assumed by the investigated class of discrete dynamic systems is fulfilled. The examples illustrating the obtained results are given.

References:

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