  We present a systematic technique to find explicit solutions of birational
maps, provided that these solutions are given in terms of elliptic functions.
The two main ingredients are: (i) application of classical addition theorems
for elliptic functions, and (ii) experimental technique to detect an algebraic
curve containing a given sequence of points in a plane. These methods are
applied to Kahan-Hirota-Kimura discretizations of the periodic Volterra chains
with 3 and 4 particles.
