The stability of the equilibrium of reversible systems
The stability of the equilibrium of reversible systems
In this paper, we consider the system \[ \dot x=a(t)y^{2m+1}+f_1(x,y,t),\quad \dot y=-b(t)x^{2n+1}+f_2(x,y,t),\] where $m,n\in \mathbf {Z}_+$, $m+n\ge 1$, $a(t)$ and $b(t)$ are continuous, even and 1-periodic in the time variable $t$; $f_1$ and $f_2$ are real analytic in a neighbourhood of the origin $(0,0)$ of $(x,y)$-plane and continuous 1-periodic in …