Repositori institucional URV
| URV's Author/s: | Ramírez Inostroza, Rafael Orlando / Ramírez Pérez, Rebeca |
| Author, as appears in the article.: | Llibre J; Ramírez R; Ramírez V |
| Author's mail: | rebeca.ramirez@estudiants.urv.cat |
| Author identifier: | 0000-0002-4958-0291 |
| Journal publication year: | 2018 |
| Publication Type: | Journal Publications |
| ISSN: | 10726691 |
| APA: | Llibre J; Ramírez R; Ramírez V (2018). Center problem for generalized Λ-Ω differential systems. Electronic Journal Of Differential Equations, 2018(184), 1-23 |
| Papper original source: | Electronic Journal Of Differential Equations. 2018 (184): 1-23 |
| Abstract: | © 2018 Texas State University. Λ-Ω differential systems are the real planar polynomial differential equations of degree m of the form (Formula presented), where Λ = Λ(x, y) and Ω = Ω(x, y) are polynomials of degree at most m − 1 such that Λ(0, 0) = Ω(0, 0) = 0. A planar vector field with linear type center can be written as a Λ-Ω system if and only if the Poincaré-Liapunov first integral is of the form F =1/2 (x2 + y2)(1 + O(x, y)). The main objective of this article is to study the center problem for Λ-Ω systems of degree m with (Formula presented), where µ, a1, a2 are constants and Ωj = Ωj (x, y) is a homogenous polynomial of degree j, for j = 2, …, m−1. We prove the following results. Assuming that m = 2, 3, 4, 5 and (Formula presented) the Λ-Ω system has a weak center at the origin if and only if these systems after a linear change of variables (x, y) → (X, Y) are invariant under the transformationsP (X, Y, t) → (−X, Y, −t). If (µ + (m − 2))(a21 + a22) = 0 and (Formula presented) = 0 then the origin is a weak center. We observe that the main difficulty in proving this result for m > 6 is related to the huge computations. |
| Link to the original source: | https://ejde.math.txstate.edu/index.html |
| Papper version: | info:eu-repo/semantics/acceptedVersion |
| licence for use: | https://creativecommons.org/licenses/by/3.0/es/ |
| Department: | Enginyeria Informàtica i Matemàtiques |
| Licence document URL: | https://repositori.urv.cat/ca/proteccio-de-dades/ |
| Thematic Areas: | Mathematics, applied Mathematics Matemática / probabilidade e estatística Interdisciplinar Ensino Engenharias iv Ciências agrárias i Ciência da computação Astronomia / física Analysis |
| Keywords: | Weak center Reeb integrating factor Poincaré-liapunov theorem Linear type center Darboux first integral |
| Entity: | Universitat Rovira i Virgili |
| Record's date: | 2024-09-07 |
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