ON THE HOMOTOPY CLASSIFICATION OF POSITIVELYHOMOGENEOUS FUNCTIONS OF THREE VARIABLES
In this paper, we study the problem of homotopy classification of the set F of positively homogeneous smooth functions in three variables whose gradients do not vanish at nonzero points.This problem is of interest in the study of periodic and bounded solutions of systems of ordinary differential equ...
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| Format: | Article |
| Language: | English |
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Petrozavodsk State University
2021-05-01
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| Series: | Проблемы анализа |
| Subjects: | |
| Online Access: | https://issuesofanalysis.petrsu.ru/article/genpdf.php?id=9970&lang=en |
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| author | E. Mukhamadiev A. N. Naimov |
| author_facet | E. Mukhamadiev A. N. Naimov |
| author_sort | E. Mukhamadiev |
| collection | DOAJ |
| description | In this paper, we study the problem of homotopy classification of the set F of positively homogeneous smooth functions in three variables whose gradients do not vanish at nonzero points.This problem is of interest in the study of periodic and bounded solutions of systems of ordinary differential equations with the main positive homogeneous nonlinearity. The subset F0 ⊂ F is presented and for any function g(x) ∈ F0, a formula for calculating the rotation γ(∇g) of its gradient ∇g(x) on the boundary of theunit ball |x|< 1 is derived. It is proved that any function from F is homotopic to some function from F0. |
| first_indexed | 2024-12-19T10:34:56Z |
| format | Article |
| id | doaj.art-e4d5d679ae0243e1911106bd906247a3 |
| institution | Directory Open Access Journal |
| issn | 2306-3424 2306-3432 |
| language | English |
| last_indexed | 2024-12-19T10:34:56Z |
| publishDate | 2021-05-01 |
| publisher | Petrozavodsk State University |
| record_format | Article |
| series | Проблемы анализа |
| spelling | doaj.art-e4d5d679ae0243e1911106bd906247a32022-12-21T20:25:39ZengPetrozavodsk State UniversityПроблемы анализа2306-34242306-34322021-05-0110(28)2677810.15393/j3.art.2021.9970ON THE HOMOTOPY CLASSIFICATION OF POSITIVELYHOMOGENEOUS FUNCTIONS OF THREE VARIABLESE. Mukhamadiev0A. N. Naimov1Vologda State UniversityVologda Institute of Law and Economics of the Federal Penitentiary ServiceIn this paper, we study the problem of homotopy classification of the set F of positively homogeneous smooth functions in three variables whose gradients do not vanish at nonzero points.This problem is of interest in the study of periodic and bounded solutions of systems of ordinary differential equations with the main positive homogeneous nonlinearity. The subset F0 ⊂ F is presented and for any function g(x) ∈ F0, a formula for calculating the rotation γ(∇g) of its gradient ∇g(x) on the boundary of theunit ball |x|< 1 is derived. It is proved that any function from F is homotopic to some function from F0.https://issuesofanalysis.petrsu.ru/article/genpdf.php?id=9970&lang=enpositively homogeneous functionhomotopyvector field rotationhomotopy classification |
| spellingShingle | E. Mukhamadiev A. N. Naimov ON THE HOMOTOPY CLASSIFICATION OF POSITIVELYHOMOGENEOUS FUNCTIONS OF THREE VARIABLES Проблемы анализа positively homogeneous function homotopy vector field rotation homotopy classification |
| title | ON THE HOMOTOPY CLASSIFICATION OF POSITIVELYHOMOGENEOUS FUNCTIONS OF THREE VARIABLES |
| title_full | ON THE HOMOTOPY CLASSIFICATION OF POSITIVELYHOMOGENEOUS FUNCTIONS OF THREE VARIABLES |
| title_fullStr | ON THE HOMOTOPY CLASSIFICATION OF POSITIVELYHOMOGENEOUS FUNCTIONS OF THREE VARIABLES |
| title_full_unstemmed | ON THE HOMOTOPY CLASSIFICATION OF POSITIVELYHOMOGENEOUS FUNCTIONS OF THREE VARIABLES |
| title_short | ON THE HOMOTOPY CLASSIFICATION OF POSITIVELYHOMOGENEOUS FUNCTIONS OF THREE VARIABLES |
| title_sort | on the homotopy classification of positivelyhomogeneous functions of three variables |
| topic | positively homogeneous function homotopy vector field rotation homotopy classification |
| url | https://issuesofanalysis.petrsu.ru/article/genpdf.php?id=9970&lang=en |
| work_keys_str_mv | AT emukhamadiev onthehomotopyclassificationofpositivelyhomogeneousfunctionsofthreevariables AT annaimov onthehomotopyclassificationofpositivelyhomogeneousfunctionsofthreevariables |