  In order to obtain functional limit theorems for heavy tailed stationary
processes arising from dynamical systems, one needs to understand the
clustering patterns of the tail observations of the process. These patterns are
well described by means of a structure called the pilling process introduced
recently in the context of dynamical systems. So far, the pilling process has
been computed only for observable functions maximised at a single repelling
fixed point. Here, we study richer clustering behaviours by considering
correlated maximal sets, in the sense that the observable is maximised in
multiple points belonging to the same orbit, and we work out explicit
expressions for the pilling process when the dynamics is piecewise linear and
expanding ($1$-dimensional and $2$-dimensional).

Dynamical Systems