  The effect of transformations analogous to those of the real-space
renormalization group are analyzed for the temporal occurrence of earthquakes.
The distribution of recurrence times turns out to be invariant under such
transformations, for which the role of the correlations between the magnitudes
and the recurrence times are fundamental. A general form for the distribution
is derived imposing only the self-similarity of the process, which also yields
a scaling relation between the Gutenberg-Richter b-value, the exponent
characterizing the correlations, and the recurrence-time exponent. This
approach puts the study of the structure of seismicity in the context of
critical phenomena.
