line in the inset on semi-logarithmic scale indicates the exponential decay ($N(t)\sim e^{-{\kappa}t}$), while the linear fit provides for escape rate $\kappa\approx0.005.$ One can estimate (Altmann, Portela & Tél 2013) the average lifetime of chaos ($\tau$) from the escape rate, $\tau\approx 1/\kappa\approx200$ days. The exponent $z$ in algebraic decay ($N(t)\sim t^{-z}$) is found to be $z\approx 0.9$ which is somewhat smaller than the actual accepted, probably universal, value ($\sim 1.5$) of chaotic transport near the remnants of the last KAM torus (Meiss 2015).

To find analytically, and also numerically, the unstable periodic orbits and their manifolds in high dimensional phase space is a challenging task. The motion in a $2N$ dimensional phase space ($N$ is the number of degrees of freedom) proceeds on a $2N-M$ dimensional surface where $M$ is the number of existing first integrals. Constructing any Poincaré surface of section in $2N-M$ dimensions, if $2N-M>3,$ yields a confused structure-less picture, since we see the projection of any remaining dimensions.

Considering that in our model the phase space has 12 dimensions, we are not able to construct and visualize a Poincaré surface. More precisely, any 2D section of the phase space has a fuzzy structure which actually shows the 