On the distance between separatrices for the discretized pendulum equation

Hocine Sellama

We consider the discretization q(t+ε)+q(t-ε)-2q(t)=ε^{2}\sin\big(q(t)\big), $\epsilon >0$ a small parameter, of the pendulum equation $q^{\prime \prime }=\sin (q)$; in system form, we have the discr…