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On the polynomial vector fields on

Published online by Cambridge University Press:  26 September 2011

Jaume Llibre  and
Yulin Zhao
Jaume Llibre
Affiliation:
Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain (jllibre@mat.uab.cat)
Yulin Zhao
Affiliation:
Department of Mathematics, Sun Yat-Sen University, Guangzhou 510275, People's Republic of China (mcszyl@mail.sysu.edu.cn)
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Abstract

Let X be a polynomial vector field of degree n on M, M = ℝm. The dynamics and the algebraic-geometric properties of the vector fields X have been studied intensively, mainly for the case when M = ℝm, and especially when n = 2. Several papers have been dedicated to the study of the homogeneous polynomial vector field of degree n on , mainly for the case where n = 2 and M = . But there are very few results on the non-homogeneous polynomial vector fields of degree n on . This paper attempts to rectify this slightly.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 141 , Issue 5 , October 2011 , pp. 1055 - 1069
Copyright
Copyright © Royal Society of Edinburgh 2011

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