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Презентация на тему The formal normal form degenerate singular points in the case of case of focus

OBJECTIVE In the work we study the problem for the case Have a normal form where Formal normal form takes the form
THE FORMAL NORMAL FORM  DEGENERATE SINGULAR POINTS  IN THE CASE OBJECTIVE In the work we study the problem for the case AIM OF WORKThe direct study of a formal normal form with the Takens in 1974 for the system of equations of the form General( for all cases) the formal normal form was obtained in 2015. THEOREM The field DEFINITION Two analytical vector fields  in THE FUNCTIONAL EQUATION OF EQUIVALENCE AND THE SCHEME OF REDUCTION TO SYSTEMS We substitute the expansions Get the system of equations. This system has a specific type which INFERENCEAfter we solve this system of equations the formal normal form takes REFERENCESFormal normal form Zholandeka Strozhinoy — PWS Publishing, 199717aliya93@mail.ru Thank you for attention!17aliya93@mail.ru
Слайды презентации

Слайд 2 OBJECTIVE
In the work we study the problem for

OBJECTIVE In the work we study the problem for the case

the case

Have a normal form where Formal normal form takes the form

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Слайд 3 AIM OF WORK
The direct study of a formal

AIM OF WORKThe direct study of a formal normal form with

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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Слайд 4 Takens in 1974 for the system of equations

Takens in 1974 for the system of equations of the form

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 5 General( for all cases) the formal normal form

General( for all cases) the formal normal form was obtained in

was obtained in 2015. This Form looks very complicated and

has the form:

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Слайд 6 THEOREM
The field

THEOREM The field       is formally

is formally equivalent

to one of the following fields formal power series. Forms are the only modulo substitutions

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Слайд 7 DEFINITION
Two analytical vector fields in

DEFINITION Two analytical vector fields in   are formally equivalent

are formally equivalent ,then and only then

when there is a formal diffeomorphisms

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Слайд 8 THE FUNCTIONAL EQUATION OF EQUIVALENCE AND THE SCHEME

THE FUNCTIONAL EQUATION OF EQUIVALENCE AND THE SCHEME OF REDUCTION TO

OF REDUCTION TO SYSTEMS OF LINEAR EQUATIONS

Objective :to find

a formal normal form as simple as possible species

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Слайд 9 We substitute the expansions

We substitute the expansions      in the main equation :17aliya93@mail.ru

in the

main equation :

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Слайд 10 Get the system of equations. This system has

Get the system of equations. This system has a specific type

a specific type which allows to solve it consistently.
tab1.
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Слайд 11 INFERENCE
After we solve this system of equations the

INFERENCEAfter we solve this system of equations the formal normal form

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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Слайд 12 REFERENCES
Formal normal form Zholandeka Strozhinoy — PWS Publishing,

REFERENCESFormal normal form Zholandeka Strozhinoy — PWS Publishing, 199717aliya93@mail.ru

1997
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