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:  0000000249580291

Journal publication year:  2018

Publication Type:  Journal Publications

ISSN:  10726691

APA:  Llibre J; Ramírez R; Ramírez V (2018). Center problem for generalized ΛΩ differential systems. Electronic Journal Of Differential Equations, 2018(184), 123

Papper original source:  Electronic Journal Of Differential Equations. 2018 (184): 123

Abstract:  © 2018 Texas State University. ΛΩ 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 ΛΩ system if and only if the PoincaréLiapunov 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 ΛΩ 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 ΛΩ 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:eurepo/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/protecciodedades/

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 Poincaréliapunov theorem Linear type center Darboux first integral

Entity:  Universitat Rovira i Virgili

Record's date:  20240907
