Quadratic three-dimensional differential systems having invariant planes with total multiplicity nine

被引：1
作者：
Llibre J. [1 ]
Messias M. [2 ]
Reinol A.C. [3 ]
机构：
[1] Departament de Matemàtiques, Universitat Autònoma de Barcelona, Barcelona, 08193 Bellaterra, Catalonia
[2] Departamento de Matemática e Computação, Faculdade de Ciências e Tecnologia, UNESP – Universidade Estadual Paulista, Presidente Prudente, SP
[3] Departamento de Matemática, Instituto de Biociências, Letras e Ciências Exatas, UNESP – Universidade Estadual Paulista, São José do Rio Preto, SP
来源：
Rendiconti del Circolo Matematico di Palermo Series 2 | 2018年 / 67卷 / 3期
基金：
巴西圣保罗研究基金会;
关键词：
Extactic polynomial; First integrals; Invariant planes; Polynomial differential systems;
D O I：
10.1007/s12215-018-0338-x
中图分类号：
学科分类号：
摘要：
In this paper we consider all the quadratic polynomial differential systems in R3 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. © 2018, Springer-Verlag Italia S.r.l., part of Springer Nature.
引用
收藏
页码：569 / 580
页数：11
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