Volume 25, Issue 3, July 2018, Pages 387 - 398
Integrability Conditions for Complex Homogeneous Kukles Systems
Authors
Jaume Giné
Departament de Matemàtica, Inspires Research Centre, Universitat de Lleida, Avda. Jaume II, 69; 25001 Lleida, Catalonia, Spain,gine@matematica.udl.cat
Claudia Valls
Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais 1049-001, Lisboa, Portugal,cvalls@math.ist.utl.pt
Received 20 December 2017, Accepted 12 February 2018, Available Online 6 January 2021.
- DOI
- 10.1080/14029251.2018.1494731How to use a DOI?
- Keywords
- Integrability; complex center-focus problem; Saddle constants; Kukles systems; Gröbner Basis
- Abstract
In this paper we study the existence of local analytic first integrals for complex polynomial differential systems of the form ẋ = x + Pn(x, y), ẏ = −y, where Pn(x,y) is a homogeneous polynomial of degree n, called the complex homogeneous Kukles systems of degree n. We characterize all the homogeneous Kukles systems of degree n that belong to the Sibirsky ideal. Finally, we provide necessary and sufficient conditions when n = 2,...,7 in order that the complex homogeneous Kukles system has a local analytic first integral computing the saddle constants and using Gröbner bases to find the decomposition of the algebraic variety into its irreducible components.
- Copyright
- © 2018 The Authors. Published by Atlantis and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Download article (PDF)
View full text (HTML)
Cite this article
TY - JOUR AU - Jaume Giné AU - Claudia Valls PY - 2021 DA - 2021/01/06 TI - Integrability Conditions for Complex Homogeneous Kukles Systems JO - Journal of Nonlinear Mathematical Physics SP - 387 EP - 398 VL - 25 IS - 3 SN - 1776-0852 UR - https://doi.org/10.1080/14029251.2018.1494731 DO - 10.1080/14029251.2018.1494731 ID - Giné2021 ER -