Journal of Nonlinear Mathematical Physics

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 = x + Pn(x, y), = −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/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
25 - 3
Pages
387 - 398
Publication Date
2021/01/06
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1080/14029251.2018.1494731How to use a DOI?
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/).

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  -