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Main Title: How One can Repair Non-integrable Kahan Discretizations. II. A Planar System with Invariant Curves of Degree 6
Author(s): Schmalian, Misha
Suris, Yuri B.
Tumarkin, Yuriy
Type: Article
Abstract: We find a novel one-parameter family of integrable quadratic Cremona maps of the plane preserving a pencil of curves of degree 6 and of genus 1. They turn out to serve as Kahan-type discretizations of a novel family of quadratic vector fields possessing a polynomial integral of degree 6 whose level curves are of genus 1, as well. These vector fields are non-homogeneous generalizations of reduced Nahm systems for magnetic monopoles with icosahedral symmetry, introduced by Hitchin, Manton and Murray. The straightforward Kahan discretization of these novel non-homogeneous systems is non-integrable. However, this drawback is repaired by introducing adjustments of order 𝑂(𝜖2) in the coefficients of the discretization, where 𝜖 is the stepsize.
Subject(s): birational maps
discrete integrable systems
elliptic pencil
integrable discretization
rational elliptic surface
Issue Date: 28-Nov-2021
Date Available: 15-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
Sponsor/Funder: DFG, 195170736, TRR 109: Diskretisierung in Geometrie und Dynamik
TU Berlin, Open-Access-Mittel – 2021
Journal Title: Mathematical Physics, Analysis and Geometry
Publisher: Springer Nature
Volume: 24
Article Number: 40
Publisher DOI: 10.1007/s11040-021-09413-2
EISSN: 1572-9656
ISSN: 1385-0172
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik » FG Dynamische Systeme
Appears in Collections:Technische Universität Berlin » Publications

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