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The formal normal form degenerate singular points in the case of case of focus Tasmukhametova Aliya Bazarbaevna scientific adviser: Voronin Sergey Mikhaylovich

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Objective In the work we study the problem for the case Have a normal form where Formal normal form takes the form

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aim of work 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.

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preface 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.

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General( for all cases) the formal normal form was obtained in 2015. This Form looks very complicated and has the form: General( for all cases) the formal normal form was obtained in 2015. This Form looks very complicated and has the form:

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Theorem The field is formally equivalent to one of the following fields formal power series. Forms are the only modulo substitutions

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definition Two analytical vector fields in are formally equivalent ,then and only then when there is a formal diffeomorphisms

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The functional equation of equivalence and the scheme of reduction to systems of linear equations Objective :to find a formal normal form as simple as possible species

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We substitute the expansions in the main equation : We substitute the expansions in the main equation :

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Get the system of equations. This system has a specific type which allows to solve it consistently. Get the system of equations. This system has a specific type which allows to solve it consistently.