On the construction of elliptic solutions of integrable birational maps
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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.
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
CitationPetrera, M., Pfadler, A., Suris, Y., Fedorov, Y. On the construction of elliptic solutions of integrable birational maps. "Experimental mathematics", 1 Gener 2017, vol. 26, núm. 3, p. 324-341.