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№1 слайд
Содержание слайда: The formal normal form
degenerate singular points
in the case of case of focus
Tasmukhametova Aliya Bazarbaevna
scientific adviser: Voronin Sergey Mikhaylovich
№2 слайд
Содержание слайда: Objective
In the work we study the problem for the case Have a normal form
where
Formal normal form takes the form
№3 слайд
Содержание слайда: 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.
№4 слайд
Содержание слайда: 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.
№5 слайд
Содержание слайда: 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:
№6 слайд
Содержание слайда: Theorem
The field is formally equivalent to one of the following fields
formal power series. Forms
are the only modulo substitutions
№7 слайд
Содержание слайда: definition
Two analytical vector fields
in are formally equivalent ,then and only then when there is a formal diffeomorphisms
№8 слайд
Содержание слайда: 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
№9 слайд
Содержание слайда: We substitute the expansions in the main equation :
We substitute the expansions in the main equation :
№10 слайд
Содержание слайда: 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.
№11 слайд
Содержание слайда: inference
After we solve this system of equations the formal normal form takes the form
№12 слайд
Содержание слайда: References
Formal normal form Zholandeka Strozhinoy — PWS Publishing, 1997
№13 слайд
Содержание слайда: Thank you for attention!