2026-04-17T03:37:44Zhttps://recercat.cat/oai/request

oai:recercat.cat:2117/1050452026-01-21T06:25:50Zcom_2072_1033col_2072_452950

On the construction of elliptic solutions of integrable birational maps Petrera, Matteo Pfadler, Andreas Suris, Yuri B. Fedorov, Yuri Àrees temàtiques de la UPC::Matemàtiques i estadística Geometry, Algebraic Elliptic functions elliptic function birational map integrable map Geometria algebraica Funcions el·líptiques 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) 2017-01-01 Article http://www.tandfonline.com/doi/full/10.1080/10586458.2016.1166354 http://creativecommons.org/licenses/by-nc-nd/3.0/es/ Open Access Attribution-NonCommercial-NoDerivs 3.0 Spain