scholarly journals Two-Dimensional Homogeneous Polynomial Vector Fields with Common Factors

1994 ◽  
Vol 181 (3) ◽  
pp. 836-863 ◽  
Author(s):  
C.B. Collins
Keyword(s):  
Homogeneous Polynomial ◽  
Vector Fields ◽  
Common Factors ◽  
Two Dimensional ◽  
Polynomial Vector ◽  
Polynomial Vector Fields

scholarly journals Centers of weight-homogeneous polynomial vector fields on the plane

2016 ◽  
Vol 145 (6) ◽  
pp. 2539-2555 ◽  
Author(s):  
Jaume Giné ◽  
Jaume Llibre ◽  
Claudia Valls
Keyword(s):  
Homogeneous Polynomial ◽  
Vector Fields ◽  
Polynomial Vector ◽  
Polynomial Vector Fields

DARBOUXIAN INTEGRABILITY OF POLYNOMIAL VECTOR FIELDS WITH SPECIAL EMPHASIS ON THE TWO-DIMENSIONAL SURFACES

2002 ◽  
Vol 12 (12) ◽  
pp. 2821-2833 ◽  
Author(s):  
JAUME LLIBRE ◽  
GERARDO RODRÍGUEZ
Keyword(s):  
Vector Fields ◽  
Two Dimensional ◽  
Polynomial Vector ◽  
Dimensional Torus ◽  
Real Polynomial ◽  
Polynomial Vector Fields

First, we present a survey on the Darbouxian theory of integrability for real polynomial vector fields in the plane. Then we extend this theory to real polynomial vector fields on two-dimensional surfaces, more specifically on the quadratics and on the two-dimensional torus.

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