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. x˙=y,y˙=P0(x)+P1(x)y+P2(x)y2, We also study the centers for the Cherkas polynomial differential systems where Pi(x) are polynomials...
| Authors: | , |
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| Format: | article |
| Status: | Published version |
| Publication Date: | 2016 |
| Country: | España |
| Institution: | Universitat de Lleida (UdL) |
| Repository: | Repositori Obert UdL |
| OAI Identifier: | oai:repositori.udl.cat:10459.1/59108 |
| Online Access: | https://doi.org/10.14232/ejqtde.2016.1.49 http://hdl.handle.net/10459.1/59108 |
| Access Level: | Open access |
| Keyword: | Center problem Analytic integrability Polynomial Cherkas differential systems |
| Summary: | 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. x˙=y,y˙=P0(x)+P1(x)y+P2(x)y2, We also study the centers for the Cherkas polynomial differential systems where Pi(x) are polynomials of degree n, P0(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. |
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