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

Author(s):  
Shi Songling
Author(s):  
Elena Celledoni ◽  
Robert I. McLachlan ◽  
David I. McLaren ◽  
Brynjulf Owren ◽  
G. R. W. Quispel

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.


Nonlinearity ◽  
2004 ◽  
Vol 18 (1) ◽  
pp. 175-209 ◽  
Author(s):  
Marcin Bobie ski ◽  
Henryk o a dek

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

Sign in / Sign up

Export Citation Format

Share Document