Quadratic three-dimensional differential systems having invariant planes with total multiplicity nine
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Messias, Marcelo (Universidade Estadual Paulista. Departamento de Matemática e Computação (Brazil))
Reinol, Alisson C. (Universidade Estadual Paulista. Instituto de Biociências, Letras e Ciências Exatas. Departamento de Matemática (Brazil))

Additional title:	Quadratic polynomial differential systems in R3 having invariant planes with total multiplicity nine
Date:	2018
Abstract:	In this paper we consider all the quadratic polynomial differential systems in R having exactly nine invariant planes taking into account their multiplicities. This is the maximum number of invariant planes that these kind of systems can have, without taking into account the infinite plane. We prove that there exist thirty possible configurations for these invariant planes, and we study the realization and the existence of first integrals for each one of these configurations. We show that at least twenty three of these configurations are realizable and provide explicit examples for each one of them.
Grants:	Ministerio de Economía y Competitividad MTM2013-40998-P Ministerio de Economía y Competitividad MTM2016-77278-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568 Ministerio de Economía y Competitividad MDM-2014-0445
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Polynomial differential systems ; Invariant planes ; First integrals ; Extactic polynomial
Published in:	Rendiconti del Circolo Matematico di Palermo, Vol. 67, Issue 3 (December 2018) , p. 569-580, ISSN 1973-4409

DOI: 10.1007/s12215-018-0338-x

Postprint 15 p, 297.8 KB

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