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
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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