Tasmukhametova Aliya Bazarbaevna
scientific adviser: Voronin Sergey Mikhaylovich
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The formal normal form degenerate singular points in the case of case of focus презентация
Содержание
- 1. The formal normal form degenerate singular points in the case of case of focus
- 2. OBJECTIVE In the work we study
- 3. AIM OF WORK The direct study of
- 4. Takens in 1974 for the system of
- 5. General( for all cases) the formal normal
- 6. THEOREM The field
- 7. DEFINITION Two analytical vector fields
- 8. THE FUNCTIONAL EQUATION OF EQUIVALENCE AND THE
- 9. We substitute the expansions
- 10. Get the system of equations. This system
- 11. INFERENCE After we solve this system of
- 12. REFERENCES Formal normal form Zholandeka Strozhinoy — PWS Publishing, 1997 17aliya93@mail.ru
- 13. Thank you for attention! 17aliya93@mail.ru
OBJECTIVE
In the work we study the problem for the case Have a normal form
where
Слайд 1THE FORMAL NORMAL FORM DEGENERATE SINGULAR POINTS IN THE CASE OF
CASE OF FOCUS
Слайд 2OBJECTIVE
In the work we study the problem for the case
Have a normal form
where
Formal normal form takes the form
17aliya93@mail.ru
Слайд 3AIM 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.
17aliya93@mail.ru
Слайд 4Takens 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.
PREFACE
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Слайд 5General( for all cases) the formal normal form was obtained in
2015.
This Form looks very complicated and has the form:
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Слайд 6THEOREM
The field
is formally equivalent to one of the following fields
formal power series. Forms
are the only modulo substitutions
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Слайд 7DEFINITION
Two analytical vector fields
in are
formally equivalent ,then and only then when there is a formal diffeomorphisms
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Слайд 8THE 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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Слайд 10Get the system of equations. This system has a specific type
which allows to solve it consistently.
tab1.
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Слайд 11INFERENCE
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.
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