scholarly journals Poincaré Compactification for Non-polynomial Vector Fields

2020 ◽  
Vol 19 (1) ◽  
Author(s):  
José Luis Bravo ◽  
Manuel Fernández ◽  
Antonio E. Teruel
Keyword(s):  
Vector Fields ◽  
Polynomial Vector ◽  
Polynomial Vector Fields ◽  
Poincaré Compactification

scholarly journals Periodic perturbations of quadratic planar polynomial vector fields

2002 ◽  
Vol 74 (2) ◽  
pp. 193-198 ◽  
Author(s):  
MARCELO MESSIAS
Keyword(s):  
Vector Fields ◽  
Dynamical Behavior ◽  
Saddle Points ◽  
Heteroclinic Cycle ◽  
Polynomial Vector ◽  
Polynomial Vector Fields ◽  
Poincaré Compactification ◽  
Stable And Unstable Manifolds ◽  
Perturbed System ◽  
Periodic Perturbations

In this work are studied periodic perturbations, depending on two parameters, of quadratic planar polynomial vector fields having an infinite heteroclinic cycle, which is an unbounded solution joining two saddle points at infinity. The global study envolving infinity is performed via the Poincaré compactification. The main result obtained states that for certain types of periodic perturbations, the perturbed system has quadratic heteroclinic tangencies and transverse intersections between the local stable and unstable manifolds of the hyperbolic periodic orbits at infinity. It implies, via the Birkhoff-Smale Theorem, in a complex dynamical behavior of the solutions of the perturbed system, in a finite part of the phase plane.

Limit cycles of three-dimensional polynomial vector fields

Nonlinearity ◽  
2004 ◽  
Vol 18 (1) ◽  
pp. 175-209 ◽  
Author(s):  
Marcin Bobie ski ◽  
Henryk o a dek
Keyword(s):  
Limit Cycles ◽  
Vector Fields ◽  
Three Dimensional ◽  
Polynomial Vector ◽  
Polynomial Vector Fields

scholarly journals Multiplicity of polynomials on trajectories of polynomial vector fields in $C^3$

1998 ◽  
Vol 44 (1) ◽  
pp. 109-121 ◽  
Author(s):  
Andrei Gabrielov ◽  
Frédéric Jean ◽  
Jean-Jacques Risler
Keyword(s):  
Vector Fields ◽  
Polynomial Vector ◽  
Polynomial Vector Fields
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