On the Construction of Elliptic Solutions of Integrable Birational Maps

Matteo Petrera, Andreas Pfadler, Yuri B. Suris, Yuri N. Fedorov

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

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 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.

Original languageEnglish
Pages (from-to)324-341
Number of pages18
JournalExperimental Mathematics
Volume26
Issue number3
DOIs
StatePublished - 3 Jul 2017
Externally publishedYes

Keywords

  • birational map
  • elliptic function
  • integrable map

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