An algorithm for providing the normal forms of spatial quasi-homogeneous polynomial differential systems
García, Belén (Universidad de Oviedo. Departamento de Matemáticas)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Lombardero, Antón (Universidad de Oviedo. Departamento de Matemáticas)
Suárez Pérez del Río, Jesús (Universidad de Oviedo. Departamento de Matemáticas)

Date:	2019
Abstract:	Quasi-homogeneous systems, and in particular those 3-dimensional, are currently a thriving line of research. But a method for obtaining all fields of this class is not yet available. The weight vectors of a quasi-homogeneous system are grouped into families. We found the maximal spatial quasi-homogeneous systems with the property of having only one family with minimum weight vector. This minimum vector is unique to the system, thus acting as identification code. We develop an algorithm that provides all normal forms of maximal 3-dimensional quasi-homogeneous systems for a given degree. All other 3-dimensional quasi-homogeneous systems can be trivially deduced from these maximal systems. We also list all the systems of this type of degree 2 using the algorithm. With this algorithm we make available to the researchers all 3-dimensional quasi-homogeneous systems.
Grants:	Ministerio de Economía y Competitividad MTM2017-87697-P Ministerio de Economía y Competitividad MTM2016-77278-P European Commission 777911 Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Quasi-homogeneous ; Polynomial differential system ; Algorithm ; Weight vector
Published in:	Journal of Symbolic Computation, Vol. 95 (November-December 2019) , p. 1-25, ISSN 0747-7171

DOI: 10.1016/j.jsc.2018.08.006

Postprint 34 p, 496.0 KB

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Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
Articles > Published articles