  The numerical optimized shooting method for finding periodic orbits in
nonlinear dynamical systems was employed to determine the existence of periodic
orbits in the well-known R\"ossler system. By optimizing the period $T$ and the
three system parameters, $a$, $b$ and $c$, simultaneously, it was found that,
for any initial condition $(x_0,y_0,z_0) \in \Re^3$, there exists at least one
set of optimized parameters corresponding to a periodic orbit passing through $
(x_0,y_0,z_0)$. After a discussion of this result it was concluded that its
analytical proof may present an interesting new mathematical challenge.
