  We study and compare three characteristic times of the standard map, the
Lyapunov time t_L, the Poincare recurrence time t_r and the stickiness (or
escape) time t_{st}. The Lyapunov time is the inverse of the Lyapunov
characteristic number LCN and in general is quite small. We find empirical
relations for the LCN as a function of the nonlinearity parameter K and of the
chaotic area A. We also find empirical relations for the Poincare recurrence
time t_r as a function of the nonlinearity parameter K, of the chaotic area A
and of the size of the box of initial conditions e. As a consequence we find
relations between t_r and LCN. We compare the distributions of the stickiness
time and the Poincare recurrence time. The stickiness time inside the sticky
regions at the boundary of the islands of stability is orders of magnitude
smaller than the Poincare recurrence time t_r and this affects the diffusion
exponent mu, which converges always to the value mu=1. This is shown in an
extreme stickiness case. The diffusion is anomalous (ballistic motion) inside
the accelerator mode islands of stability with mu=2 but it is normal everywhere
outside the islands with mu=1. In a particular case of extreme stickiness we
find the hierarchy of islands around islands.
