Non-standard discretizations of a Hamiltonian system related to the fourth Painlevé equation

Galina Filipuk, Thomas Kecker

Research output: Chapter in Book/Report/Conference proceedingChapter (peer-reviewed)peer-review


We consider non-standard discretizations of a cubic, non-autonomous Hamiltonian system, studied by the authors in an earlier article, related to the fourth Painlevé equation (a class of integrable, second-order non-linear, non-autonomous differential equations). Discretizing a differential system is a non-unique process and we employ different methods such as the (symmetric) Kahan method and a more general class of discretizations by introducing further parameters to the equations, with the aim of reducing the algebraic entropy of the system, which is a measure of complexity of the solutions of the system. Integrability of discrete systems is usually associated with zero algebraic entropy. Using the concept of singularity confinement, we can identify the cases which have reduced, though non-zero, algebraic entropy as compared with generic discretization.
Original languageEnglish
Title of host publicationFormal and Analytic Solutions of Differential Equations
EditorsGalina Filipuk, Alberto Lastra, Sławomir Michalik
PublisherWorld Scientific
Number of pages20
ISBN (Electronic)9781800611375
ISBN (Print)9781800611351
Publication statusPublished - 1 Feb 2022


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