Analytic reducibility of nondegenerate centers: Cherkas systems
In this paper we study the center problem for polynomial differential systems and we prove that any center of an analytic differential system is analytically reducible. We also study the centers for the Cherkas polynomial differential systems \[ \dot{x}=y, \qquad \dot{y}=P_0(x)+P_1(x)y+P_2(x)y^2, \]...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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University of Szeged
2016-07-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=4425 |
| _version_ | 1797830601749823488 |
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| author | Jaume Giné Jaume Llibre |
| author_facet | Jaume Giné Jaume Llibre |
| author_sort | Jaume Giné |
| collection | DOAJ |
| description | In this paper we study the center problem for polynomial differential systems and we prove that any center of an analytic differential system is analytically reducible. We also study the centers for the Cherkas polynomial differential systems
\[
\dot{x}=y, \qquad \dot{y}=P_0(x)+P_1(x)y+P_2(x)y^2,
\]
where $P_i(x)$ are polynomials of degree $n$, $P_0(0)=0$ and $P_0'(0) <0$. Computing the focal values we find the center conditions for such systems for degree $3$, and using modular arithmetics for degree $4$. Finally we do a conjecture about the center conditions for Cherkas polynomial differential systems of degree $n$. |
| first_indexed | 2024-04-09T13:38:43Z |
| format | Article |
| id | doaj.art-c0f7cd6dc8884d0ea87b5a0e41798ae9 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:38:43Z |
| publishDate | 2016-07-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-c0f7cd6dc8884d0ea87b5a0e41798ae92023-05-09T07:53:05ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752016-07-0120164911010.14232/ejqtde.2016.1.494425Analytic reducibility of nondegenerate centers: Cherkas systemsJaume Giné0Jaume Llibre1Universidad de Lleida, Lleida, Catalonia, SpainDepartament de Matemàtiques, Universitat Autònoma de Barcelona, SpainIn this paper we study the center problem for polynomial differential systems and we prove that any center of an analytic differential system is analytically reducible. We also study the centers for the Cherkas polynomial differential systems \[ \dot{x}=y, \qquad \dot{y}=P_0(x)+P_1(x)y+P_2(x)y^2, \] where $P_i(x)$ are polynomials of degree $n$, $P_0(0)=0$ and $P_0'(0) <0$. Computing the focal values we find the center conditions for such systems for degree $3$, and using modular arithmetics for degree $4$. Finally we do a conjecture about the center conditions for Cherkas polynomial differential systems of degree $n$.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=4425center problemanalytic integrabilitypolynomial cherkas differential systems |
| spellingShingle | Jaume Giné Jaume Llibre Analytic reducibility of nondegenerate centers: Cherkas systems Electronic Journal of Qualitative Theory of Differential Equations center problem analytic integrability polynomial cherkas differential systems |
| title | Analytic reducibility of nondegenerate centers: Cherkas systems |
| title_full | Analytic reducibility of nondegenerate centers: Cherkas systems |
| title_fullStr | Analytic reducibility of nondegenerate centers: Cherkas systems |
| title_full_unstemmed | Analytic reducibility of nondegenerate centers: Cherkas systems |
| title_short | Analytic reducibility of nondegenerate centers: Cherkas systems |
| title_sort | analytic reducibility of nondegenerate centers cherkas systems |
| topic | center problem analytic integrability polynomial cherkas differential systems |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=4425 |
| work_keys_str_mv | AT jaumegine analyticreducibilityofnondegeneratecenterscherkassystems AT jaumellibre analyticreducibilityofnondegeneratecenterscherkassystems |