To avoid the problem connected with the choice of different \Omega, \omega, and M for our test particles (see the section on asymmetries), we used another set of initial conditions, in which all particles have same a, \Omega, \omega, and M as Kiviuq, and different values of eccentricities and \Theta=(1-e²)cos²I.   Our initial conditions covers a grid in \Theta and e_max, which are two integrals of the secular problem, that goes from 0.3 to 0.67 for \Theta, with a step of 0.02, and from 0 to 0.6 in e, with a step of 0.03.  The inclinations are derived from the values of \Theta and e.  In the following plots we reports particles fate and contour plot of \sigma for a simulation involving Jupiter and Saturn.
 

In the following plots we report particles fate and contour plots of \sigma for an integration done using the SEC Bretagnon solution
 

Finally, we report the results of an integration with the Lyapunov integrator in the following figure, that shows the contour plot of Lyapunov times.The blue regions are clearly associated with the chaotic regions found with FAM.  The red region seems to be associated with the secondary resonance involving the great-inequality.    The second picture shows the results of a simulation with the SEC solution of the Bretagnon model.