  We consider the orbits in the Yang-Mills (YM) potential V=1/2 x2 y2 and in
the potentials of the general form Vg=1/2 [{\alpha} (x2 +y2)+x2 y2]. The stable
period-9 (number of intersection with the x-axis, with ) orbit found in the YM
potential is a bifurcation of a basic period-9 orbit of the Vg potential for a
value of {\alpha} slightly above zero. This basic period-9 family and its
bifurcations exist only up to a maximum value of {\alpha}={\alpha}max. We
calculate the Henon stability index of these orbits. The pattern of the
stability diagram is the same for all the symmetric orbits of odd periods
3,5,7,9 and 11. We also found the stability diagrams for asymmetric orbits of
period 2,3,4,5 which have again the same pattern. All these orbits are unstable
for {\alpha}=0 (YM potential). These new results indicate that in the YM
potential the only stable orbits are those of period-9 and some orbits with
multiples of 9 periods.

Chaotic Dynamics