| Contents |
| Periodic difference equations of the form
$$
x_{n+1}=f_{n\, mod p}(x_n),
$$
where each $f_j$ is a continuous interval map,
$j=0,1,\ldots,p-1$, appear in a natural way in technical and social sciences,
related to processes involving two or more interactions so that for the
knowledge of the behaviour of these systems it is necessary to alternate
different discrete dynamical systems corresponding to each period of the
process. In this sense, it is interesting to stress that the above equations
can model, for instance, certain populations in a periodically fluctuating environment.
In the present talk we discuss the notion of folding and unfolding related
to this type of non-autonomous equations. It is possible to glue certain
maps of this equation to shorten its period, which we call folding. On the
other hand, we can unfold the glued maps so the original structure can be
recovered or understood. We focus on the periodic structure under
the effect of folding and unfolding: we analyze the relationship between
the periods of periodic sequences of the $p$-periodic difference equation
and the periods of the corresponding subsequences related to the folded systems. |
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