2026-04-14T02:38:08Zhttps://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 Universitat Politècnica de Catalunya. Departament de Matemàtiques Universitat Politècnica de Catalunya. SD - Sistemes Dinàmics de la UPC 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 Petrera, 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. 1058-6458 https://hdl.handle.net/2117/105045 10.1080/10586458.2016.1166354 eng 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 18 p. application/pdf