scholarly journals A class of polynomial planar vector fields with polynomial first integral

2015 ◽  
Vol 430 (1) ◽  
pp. 354-380 ◽  
Author(s):  
A. Ferragut ◽  
C. Galindo ◽  
F. Monserrat
Keyword(s):  
Vector Fields ◽  
First Integral ◽  
Planar Vector Fields ◽  
Polynomial First Integral ◽  
Planar Vector

A note on analytic integrability of planar vector fields

2012 ◽  
Vol 23 (5) ◽  
pp. 555-562 ◽  
Author(s):  
A. ALGABA ◽  
C. GARCÍA ◽  
M. REYES
Keyword(s):  
Vector Field ◽  
Integrable Systems ◽  
Analytic Functions ◽  
Vector Fields ◽  
First Integral ◽  
Analytic Integrability ◽  
Planar Vector Fields ◽  
Planar Vector ◽  
Analytic First Integral ◽  
Image Position

We give a new characterisation of integrability of a planar vector field at the origin. This allows us to prove that the analytic systemswhereh,K, Ψ and ξ are analytic functions defined in the neighbourhood ofOwithK(O) ≠ 0 or Ψ(O) ≠ 0 andn≥ 1, have a local analytic first integral at the origin. We show new families of analytically integrable systems that are held in the above class. In particular, this class includes all the nilpotent and generalised nilpotent integrable centres that we know.

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.

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
Sign in / Sign up

Export Citation Format

Share Document