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dc.contributor.authorSchmalian, Misha
dc.contributor.authorSuris, Yuri B
dc.contributor.authorTumarkin, Yuriy
dc.date.accessioned2021-12-15T12:13:37Z
dc.date.available2021-12-15T12:13:37Z
dc.date.issued2021-12
dc.date.submitted2021-07-07
dc.identifier.citationMathematical Physics, Analysis and Geometry, volume 24, issue 4, page 40
dc.identifier.issn1385-0172
dc.identifier.others11040-021-09413-2
dc.identifier.other9413
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/331500
dc.description.abstract<jats:title>Abstract</jats:title><jats:p>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 <jats:inline-formula><jats:alternatives><jats:tex-math>$$O(\epsilon ^2)$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo>(</mml:mo> <mml:msup> <mml:mi>ϵ</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> in the coefficients of the discretization, where <jats:inline-formula><jats:alternatives><jats:tex-math>$$\epsilon $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ϵ</mml:mi> </mml:math></jats:alternatives></jats:inline-formula> is the stepsize.</jats:p>
dc.languageen
dc.publisherSpringer Science and Business Media LLC
dc.subjectArticle
dc.subjectBirational maps
dc.subjectDiscrete integrable systems
dc.subjectElliptic pencil
dc.subjectRational elliptic surface
dc.subjectIntegrable discretization
dc.titleHow One can Repair Non-integrable Kahan Discretizations. II. A Planar System with Invariant Curves of Degree 6
dc.typeArticle
dc.date.updated2021-12-15T12:13:36Z
prism.publicationNameMathematical Physics, Analysis and Geometry
dc.identifier.doi10.17863/CAM.78954
dcterms.dateAccepted2021-10-28
rioxxterms.versionofrecord10.1007/s11040-021-09413-2
rioxxterms.versionVoR
rioxxterms.licenseref.urihttp://creativecommons.org/licenses/by/4.0/
dc.contributor.orcidSuris, Yuri B [0000-0001-9378-0314]
dc.identifier.eissn1572-9656
pubs.funder-project-iddeutsche forschungsgemeinschaft (TRR 109)
cam.issuedOnline2021-11-28


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