Fig. 12.

Behaviour of (33) on the Poincaré disc for $\epsilon =0$, along the curve $A_{\ell }(C)=-\frac{1}{16}+\frac{C}{4}$. At $C=\frac{1}{2}$, the point $p_a$ connects to the SN point $p_{\pm }$. For $C<\frac{1}{2}$ the $p_a$ connects to the node $p_{-}$, for $C>\frac{1}{2}$, there is a sequence of two heteroclinic connections from $p_a$ to $p_n$, via the saddle $p_{+}$, which is resonant at $C=\frac{3}{4}$