On the construction of elliptic solutions of integrable birational maps

Abstract

This is an Accepted Manuscript of an article published by Taylor & Francis in “Experimental mathematics” on 24th August 2016, available online: http://www.tandfonline.com/doi/full/10.1080/10586458.2016.1166354

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 the following: (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 three and four particles.

Peer Reviewed

Postprint (author's final draft)