Algebraic classification of homogeneous polynomial vector fields in the plane

1996 ◽  
Vol 13 (1) ◽  
pp. 63-91 ◽  
Author(s):  
C. B. Collins
Keyword(s):  
Homogeneous Polynomial ◽  
Vector Fields ◽  
Polynomial Vector ◽  
Polynomial Vector Fields ◽  
Algebraic Classification

scholarly journals Finitely curved orbits of complex polynomial vector fields

2007 ◽  
Vol 79 (1) ◽  
pp. 13-16
Author(s):  
Albetã C. Mafra
Keyword(s):  
Vector Field ◽  
Gaussian Curvature ◽  
Algebraic Curve ◽  
Vector Fields ◽  
Complex Polynomial ◽  
Holomorphic Foliations ◽  
Holomorphic Curve ◽  
Polynomial Vector ◽  
Polynomial Vector Fields

This note is about the geometry of holomorphic foliations. Let X be a polynomial vector field with isolated singularities on C². We announce some results regarding two problems: 1. Given a finitely curved orbit L of X, under which conditions is L algebraic? 2. If X has some non-algebraic finitely curved orbit L what is the classification of X? Problem 1 is related to the following question: Let C <FONT FACE=Symbol>Ì</FONT> C² be a holomorphic curve which has finite total Gaussian curvature. IsC contained in an algebraic curve?

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
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