Integrability and linearizability of a family of three-dimensional quadratic systems
Aziz, Waleed (Salahaddin University-Erbil. Department of Mathematics (Iraq))
Amen, Azad (University of Raparin. College of Basic Education (Iraq))
Pantazi, Chara (Universitat Politècnica de Catalunya. Departament de Matemàtiques)

Date:	2021
Abstract:	We consider a three-dimensional vector field with quadratic nonlinearities and in general none of the axis plane is invariant. For our investigation, we are interesting in the case of (Formula presented. )-resonance at the origin. Hence, we deal with a nine parametric family of quadratic systems and our purpose is to understand the mechanisms of local integrability. By computing some obstructions, knowing as resonant focus quantities, first we present necessary conditions that guarantee the existence of two independent local first integrals at the origin. For this reason Gröbner basis and some other algorithms are employed. Then we examine the cases where the origin is linearizable. Some techniques like existence of invariant surfaces and Jacobi multipliers, Darboux method, properties of linearizable nodes of two dimensional systems and power series arguments are used to prove the sufficiency of the obtained conditions. For a particular three-parametric subfamily, we provide conditions on the parameters to guarantee the non-existence of a polynomial first integral.
Grants:	Agencia Estatal de Investigación PID2019-104658GB-I00 Agencia Estatal de Investigación PGC2018-098676-B-I00 Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1049
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Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Integrability ; Linearizability ; First integral ; Jacobi multiplier ; Darboux function
Published in:	Dynamical Systems, Vol. 36, Issue 2 (2021) , p. 317-331, ISSN 1468-9375

DOI: 10.1080/14689367.2021.1893661

Postprint 15 p, 305.8 KB

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