$q\left(  t=0\right)  =-\mu$ and $\dot{q}\left(  t=0\right)  =v_{0}$, a Poincaré section [@Bir] is represented vol. II, page 268) as the half line $q=-\mu^{+}$ and $\dot{q}>0$ [@And]. The symbol $+$ means that we are considering that the section is taken immediately after the kick. Due to friction during a complete cycle, a loss of velocity $-4\mu$ occurs. By considering the velocity, $v_{n}=\dot
{q}\left(  2n\pi^{+}\right)  $, at the Poincaré section in each cycle, the non-linear discrete dynamical system [@And] is obtained $$v_{n+1}=\sqrt{\left(  v_{n}-4\mu\right)  ^{2}+h^{2}}\text{.} \label{recu}%$$ This equation has the asymptotically stable fixed point $$v_{f}=\frac{h^{2}}{8\mu}+2\mu\text{.}%$$ Any initial condition $v_{0}\in\left(  4\mu,+\infty\right)  $ is attracted to $v_{f}$. Each cycle corresponds to a phase increment of $2\pi$ and the phase $\varphi$ is linear with respect to $t$, precisely $$\varphi=2\pi t.$$ As already mentioned, the nature of limit cycle is not of fundamental importance when we consider the interaction of three identical clocks, as we shall see in the sequel. We have presented here the basis of our reasonings in the non-usual case when the computations of the limit cycle are explicit and the usual angular phase is a linear function of $t$.

Two interacting oscillators
---------------------------

We present briefly the conclusions of considering two pendulum clocks suspended 