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In this work we focus on the chaotic diffusion in the phase space of a
triaxial potential resembling an elliptical galaxy. The transport
process is studied in two different action-like starting spaces in
order to cope with circulating and non-circulating orbits. Estimates
of the diffusion rate obtained by means of the variance approach are
discussed in detail and their limitations are exposed. After
revisiting the Shannon-entropy-based method from a conceptual point of
view in the framework of simple arguments taken from the information
theory, we apply it to measure changes in the unperturbed actions or
integrals of motion of the system for different sets of small
ensembles of random initial conditions. For such sets of ensembles,
estimates of the Lyapunov times are also provided. The results show
that, within the chaotic component of the phase space, the Lyapunov
times are shorter than any physical timescale as the Hubble time, but
the diffusion times are much larger than the latter. Thus we conclude
that stable chaos dominates the dynamics of realistic galactic models.