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arXiv · 1409.1741

On the construction of elliptic solutions of integrable birational maps

Matteo Petrera·Andreas Pfadler·Yuri B. Suris
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Abstract

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.

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Matteo Petrera, Andreas Pfadler, Yuri B. Suris. 2014-09-05. On the construction of elliptic solutions of integrable birational maps. https://doi.org/10.1080/10586458.2016.1166354

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