Geometric Properties of Homogeneous Vector Fields of Degree Two in R 3

1981 ◽  
Vol 268 (1) ◽  
pp. 79 ◽  
Author(s):  
M. Izabel T. Camacho
Keyword(s):  
Vector Fields ◽  
Geometric Properties ◽  
Homogeneous Vector Fields ◽  
Homogeneous Vector

Structural stability of planar quasi-homogeneous vector fields

2018 ◽  
Vol 468 (1) ◽  
pp. 212-226 ◽  
Author(s):  
A. Algaba ◽  
N. Fuentes ◽  
E. Gamero ◽  
C. Garcia
Keyword(s):  
Structural Stability ◽  
Vector Fields ◽  
Homogeneous Vector Fields ◽  
Homogeneous Vector

ON INTEGRABILITY OF DIFFERENTIAL EQUATIONS DEFINED BY THE SUM OF HOMOGENEOUS VECTOR FIELDS WITH DEGENERATE INFINITY

2001 ◽  
Vol 11 (03) ◽  
pp. 711-722 ◽  
Author(s):  
J. CHAVARRIGA ◽  
I. A. GARCÍA ◽  
J. GINÉ
Keyword(s):  
Vector Fields ◽  
Short Proof ◽  
Angular Speed ◽  
Darboux Integrability ◽  
Arbitrary Degree ◽  
Projective Techniques ◽  
Points Of View ◽  
Homogeneous Vector Fields ◽  
Integrating Factors ◽  
Homogeneous Vector

The paper deals with polynomials systems with degenerate infinity from different points of view. We show the utility of the projective techniques for such systems, and a more detailed study in the quadratic and cubic cases is carried out. On the other hand, some results on Darboux integrability in the affine plane for a class of systems are given. In short we show the explicit form of generalized Darboux inverse integrating factors for the above kind of systems. Finally, a short proof of the center cases for arbitrary degree homogeneous systems with degenerate infinity is given, and moreover we solve the center problem for quartic systems with degenerate infinity and constant angular speed.

Global stabilizability of homogeneous vector fields of odd degree

1988 ◽  
Vol 10 (4) ◽  
pp. 251-256 ◽  
Author(s):  
Alessandra Andreini ◽  
Andrea Bacciotti ◽  
Gianna Stefani
Keyword(s):  
Vector Fields ◽  
Odd Degree ◽  
Homogeneous Vector Fields ◽  
Homogeneous Vector
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