Linearization of smooth planar vector fields around singular points via commuting flows

2008 ◽  
Vol 7 (6) ◽  
pp. 1415-1428 ◽  
Author(s):  
Isaac A. García ◽  
◽  
Jaume Giné ◽  
Susanna Maza ◽  
Keyword(s):  
Vector Fields ◽  
Singular Points ◽  
Commuting Flows ◽  
Planar Vector Fields ◽  
Planar Vector

scholarly journals Separatrices at singular points of planar vector fields

1980 ◽  
Vol 145 (0) ◽  
pp. 47-78 ◽  
Author(s):  
Stephen Schecter ◽  
Michael F. Singer
Keyword(s):  
Vector Fields ◽  
Singular Points ◽  
Planar Vector Fields ◽  
Planar Vector

scholarly journals Erratum to: Separatrices at singular points of planar vector fields

1983 ◽  
Vol 151 (0) ◽  
pp. 297-298
Author(s):  
Stephen Schecter ◽  
Michael F. Singer
Keyword(s):  
Vector Fields ◽  
Singular Points ◽  
Planar Vector Fields ◽  
Planar Vector

scholarly journals A SURVEY ON THE BLOW UP TECHNIQUE

2011 ◽  
Vol 21 (11) ◽  
pp. 3103-3118 ◽  
Author(s):  
MARÍA JESÚS ÁLVAREZ ◽  
ANTONI FERRAGUT ◽  
XAVIER JARQUE
Keyword(s):  
Vector Fields ◽  
Blow Up ◽  
Singular Points ◽  
Planar Vector Fields ◽  
Different Types ◽  
Planar Vector

The blow up technique is widely used in desingularization of degenerate singular points of planar vector fields. In this survey, we give an overview of the different types of blow up and we illustrate them with many examples for better understanding. Moreover, we introduce a new generalization of the classical blow up.

scholarly journals A New Normal Form for Monodromic Nilpotent Singularities of Planar Vector Fields

2021 ◽  
Vol 18 (5) ◽  
Author(s):  
Antonio Algaba ◽  
Cristóbal García ◽  
Jaume Giné
Keyword(s):  
Normal Form ◽  
Vector Fields ◽  
New Technique ◽  
Center Problem ◽  
New Normal ◽  
Planar Vector Fields ◽  
Planar Vector ◽  
A New Technique

AbstractIn this work, we present a new technique for solving the center problem for nilpotent singularities which consists of determining a new normal form conveniently adapted to study the center problem for this singularity. In fact, it is a pre-normal form with respect to classical Bogdanov–Takens normal formal and it allows to approach the center problem more efficiently. The new normal form is applied to several examples.

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