Tasmukhametova Aliya Bazarbaevna scientific adviser: Voronin Sergey Mikhaylovich
In the work we study the problem for the case Have a normal form where Formal normal form takes the form 17 aliya 93@mail. ru 2
The direct study of a formal normal form with the feature type Bogdanov-Takens for a particular case, for the purpose of comparison with the results of Zolondek. Strozhinoi. 17 aliya 93@mail. ru 3
Takens in 1974 for the system of equations of the form got a fairly simple formal normal form but this formal normal form admits of further simplification. 17 aliya 93@mail. ru 4
General( for all cases) the formal normal form was obtained in 2015. This Form looks very complicated and has the form: 17 aliya 93@mail. ru 5
The field is formally equivalent to one of the following fields formal power series. Forms are the only modulo substitutions 17 aliya 93@mail. ru 6
Two analytical vector fields in are formally equivalent , then and only then when there is a formal diffeomorphisms 17 aliya 93@mail. ru 7
Objective : to find a formal normal form as simple as possible species 17 aliya 93@mail. ru 8
We substitute the expansions in the main equation : 17 aliya 93@mail. ru 9
Get the system of equations. This system has a specific type which allows to solve it consistently. tab 1. 17 aliya 93@mail. ru 10
After we solve this system of equations the formal normal form takes the form We have 3 adjacent degree - 3 monoms from a formal normal form. Thus , our result is consistent with the result of Zolondek. Strozhinoi. 17 aliya 93@mail. ru 11
1. Formal normal form Zholandeka Strozhinoy — PWS Publishing, 1997 17 aliya 93@mail. ru 12
Thank you for attention! 17 aliya 93@mail. ru 13
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