Commutation Relations and Discrete Garnier Systems

We present four classes of nonlinear systems which may be considered discrete analogues of the Garnier system. These systems arise as discrete isomonodromic deformations of systems of linear difference equations in which the associated Lax matrices are presented in a factored form. A system of discr...

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Опубліковано в: :Symmetry, Integrability and Geometry: Methods and Applications
Дата:2016
Автори: Ormerod, C.M., Rains, E.M.
Формат: Стаття
Мова:English
Опубліковано: Інститут математики НАН України 2016
Онлайн доступ:https://nasplib.isofts.kiev.ua/handle/123456789/148532
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:Commutation Relations and Discrete Garnier Systems / C. M. Ormerod, E. M. Rains // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 56 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-148532
record_format dspace
spelling Ormerod, C.M.
Rains, E.M.
2019-02-18T14:48:18Z
2019-02-18T14:48:18Z
2016
Commutation Relations and Discrete Garnier Systems / C. M. Ormerod, E. M. Rains // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 56 назв. — англ.
1815-0659
2010 Mathematics Subject Classification: 39A10; 39A13; 37K15
DOI:10.3842/SIGMA.2016.110
https://nasplib.isofts.kiev.ua/handle/123456789/148532
We present four classes of nonlinear systems which may be considered discrete analogues of the Garnier system. These systems arise as discrete isomonodromic deformations of systems of linear difference equations in which the associated Lax matrices are presented in a factored form. A system of discrete isomonodromic deformations is completely determined by commutation relations between the factors. We also reparameterize these systems in terms of the image and kernel vectors at singular points to obtain a separate birational form. A distinguishing feature of this study is the presence of a symmetry condition on the associated linear problems that only appears as a necessary feature of the Lax pairs for the least degenerate discrete Painlevé equations.
The work of EMR was partially supported by the National Science Foundation under the grant DMS-1500806.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Commutation Relations and Discrete Garnier Systems
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Commutation Relations and Discrete Garnier Systems
spellingShingle Commutation Relations and Discrete Garnier Systems
Ormerod, C.M.
Rains, E.M.
title_short Commutation Relations and Discrete Garnier Systems
title_full Commutation Relations and Discrete Garnier Systems
title_fullStr Commutation Relations and Discrete Garnier Systems
title_full_unstemmed Commutation Relations and Discrete Garnier Systems
title_sort commutation relations and discrete garnier systems
author Ormerod, C.M.
Rains, E.M.
author_facet Ormerod, C.M.
Rains, E.M.
publishDate 2016
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
description We present four classes of nonlinear systems which may be considered discrete analogues of the Garnier system. These systems arise as discrete isomonodromic deformations of systems of linear difference equations in which the associated Lax matrices are presented in a factored form. A system of discrete isomonodromic deformations is completely determined by commutation relations between the factors. We also reparameterize these systems in terms of the image and kernel vectors at singular points to obtain a separate birational form. A distinguishing feature of this study is the presence of a symmetry condition on the associated linear problems that only appears as a necessary feature of the Lax pairs for the least degenerate discrete Painlevé equations.
issn 1815-0659
url https://nasplib.isofts.kiev.ua/handle/123456789/148532
citation_txt Commutation Relations and Discrete Garnier Systems / C. M. Ormerod, E. M. Rains // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 56 назв. — англ.
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AT rainsem commutationrelationsanddiscretegarniersystems
first_indexed 2025-12-07T13:15:48Z
last_indexed 2025-12-07T13:15:48Z
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