2026-04-13T13:24:15Zhttps://recercat.cat/oai/requestoai:recercat.cat:10459.1/728072024-12-05T21:21:39Zcom_2072_3622col_2072_479130
RECERCAT
author
Giné, Jaume
author
Valls, Claudia
2024-12-05T21:21:39Z
2024-12-05T21:21:39Z
2022-01-24T09:19:52Z2022-01-24T09:19:52Z2018
http://hdl.handle.net/10459.1/72807
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.The first author is partially supported by a MINECO/ FEDER grant number 2017-84383-P and an AGAUR (Generalitat de Catalunya) grant number 2017SGR 1276. The second author is partially supported by FCT/Portugal through UID/MAT/04459/2013.
cc-by-nc (c) Jaume Giné, Claudia Valls, 2018 info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by-nc/4.0/
Integrability
Complex center-focus problem
Saddle constants
Kukles systems
Gröbner Basis
Integrability Conditions for Complex Homogeneous Kukles Systems
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion