On the finiteness of certain boundary cycles for NTH degree polynomial vector fields

1990 ◽  
pp. 369-372
Author(s):  
Shi Songling
Keyword(s):  
Vector Fields ◽  
Polynomial Vector ◽  
Polynomial Vector Fields ◽  
Degree Polynomial

scholarly journals Discretization of polynomial vector fields by polarization

2015 ◽  
Vol 471 (2184) ◽  
pp. 20150390 ◽  
Author(s):  
Elena Celledoni ◽  
Robert I. McLachlan ◽  
David I. McLaren ◽  
Brynjulf Owren ◽  
G. R. W. Quispel
Keyword(s):  
Vector Fields ◽  
Integration Method ◽  
Hamiltonian Vector ◽  
Polynomial Vector ◽  
Polynomial Vector Fields ◽  
Degree Polynomial ◽  
Quadratic Vector Fields ◽  
Hamiltonian Vector Fields ◽  
Quadratic Hamiltonian

A novel integration method for quadratic vector fields was introduced by Kahan in 1993. Subsequently, it was shown that Kahan's method preserves a (modified) measure and energy when applied to quadratic Hamiltonian vector fields. Here we generalize Kahan's method to cubic resp. higher degree polynomial vector fields and show that the resulting discretization also preserves modified versions of the measure and energy when applied to cubic resp. higher degree polynomial Hamiltonian vector fields.

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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