Birth of limit cycles for a class of continuous and discontinuous differential systems in (d+2)-dimension

J. Llibre, M. A. Teixeira, I. O. Zeli

The orbits of the reversible differential system $\dot{x}=-y$, $\dot{y}=x$, $\dot{z}=0$, with $x,y\in R$ and $z\in R^d$, are periodic with the exception of the equilibrium points…