  We study the global and the local transport and diffusion in the case of the
standard map, by calculating the diffusion exponent $\mu$. In the global case
we find that the mean diffusion exponent for the whole phase space is either
$\mu=1$, denoting normal diffusion or $\mu=2$ denoting anomalous diffusion (and
ballistic motion). The mean diffusion of the whole phase space is normal when
no accelerator mode exist and it is anomalous (ballistic) when accelerator mode
islands exist even if their area is tiny in the phase space. The local value of
the diffusion exponent inside the normal islands of stability is $\mu=0$, while
inside the accelerator mode islands it is $\mu=2$. The local value of the
diffusion exponent in the chaotic region outside the islands of stability
converges always to the value of 1. The time of convergence can be very long,
depending on the distance from the accelerator mode islands and the value of
the non linearity parameter $K$. For some values of $K$ the stickiness around
the accelerator mode islands is maximum and initial conditions inside the
sticky region can be dragged in a ballistic motion for extremely long times of
the order of $10^7$ or more but they will finally end up in normal mode
diffusion with $\mu=1$. We study, in particular, cases with maximum stickiness
and cases where normal and accelerator mode islands coexist. We find general
analytical solutions of periodic orbits of accelerator type and we give
evidence that they are much more numerous than the normal periodic orbits.
Thus, we expect that in every small interval $\Delta K$ of the non linearity
parameter $K$ of the standard map there exist smaller intervals of accelerator
mode islands. However, these smaller intervals are in general very small, so
that in the majority of the values of $K$ the global diffusion is normal.
