the case
Have a normal form where Formal normal form takes the form17aliya93@mail.ru
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Презентация на тему The formal normal form degenerate singular points in the case of case of focus
Содержание
- 2. Objective In the work we study the
- 3. aim of workThe direct study of a
- 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 in
- 8. The functional equation of equivalence and the
- 9. We substitute the expansions
- 10. Get the system of equations. This system
- 11. inferenceAfter we solve this system of equations
- 12. ReferencesFormal normal form Zholandeka Strozhinoy — PWS Publishing, 199717aliya93@mail.ru
- 13. Скачать презентацию
- 14. Похожие презентации
Objective In the work we study the problem for the case Have a normal form where Formal normal form takes the form
Слайд 3
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.17aliya93@mail.ru
Слайд 4 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.preface
17aliya93@mail.ru
Слайд 5 General( for all cases) the formal normal form
was obtained in 2015. This Form looks very complicated and
has the form:17aliya93@mail.ru
Слайд 6
Theorem
The field
is formally equivalent
to one of the following fields formal power series. Forms are the only modulo substitutions17aliya93@mail.ru
Слайд 7
definition
Two analytical vector fields
in
are formally equivalent ,then and only then
when there is a formal diffeomorphisms17aliya93@mail.ru
Слайд 8 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
17aliya93@mail.ru
Слайд 10 Get the system of equations. This system has
a specific type which allows to solve it consistently.
tab1.
17aliya93@mail.ru
Слайд 11
inference
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.17aliya93@mail.ru
