English

Discrete Painlev\'e Equations

Classical Analysis and ODEs 2020-02-26 v2 Exactly Solvable and Integrable Systems

Abstract

This expository article written for the Notices of the American Mathematical Society provides an overview of transcendental functions arising as solutions of the discrete Painlev\'e equations, for which the developments of the last two decades have been rich and dynamic. These equations arise at the center of many viewpoints: random matrix theory, algebra, algebraic geometry, dynamical systems and the theory of transcendental functions. The purpose of this article is to reveal this confluence and modern perspectives on it.

Keywords

Cite

@article{arxiv.1912.08959,
  title  = {Discrete Painlev\'e Equations},
  author = {Nalini Joshi},
  journal= {arXiv preprint arXiv:1912.08959},
  year   = {2020}
}

Comments

11 pages; 10 figures; to appear in Notices of the AMS. Figure 1 has been modified and rotated

R2 v1 2026-06-23T12:50:29.257Z