Laurent Polynomials and Superintegrable Maps
This article is dedicated to the memory of Vadim Kuznetsov, and begins with some of the author's recollections of him. Thereafter, a brief review of Somos sequences is provided, with particular focus being made on the integrable structure of Somos-4 recurrences, and on the Laurent property. Sub...
Saved in:
| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2007 |
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2007
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147785 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Laurent Polynomials and Superintegrable Maps / A.N.W. Hone // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 68 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862730409068986368 |
|---|---|
| author | Hone, A.N.W. |
| author_facet | Hone, A.N.W. |
| citation_txt | Laurent Polynomials and Superintegrable Maps / A.N.W. Hone // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 68 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | This article is dedicated to the memory of Vadim Kuznetsov, and begins with some of the author's recollections of him. Thereafter, a brief review of Somos sequences is provided, with particular focus being made on the integrable structure of Somos-4 recurrences, and on the Laurent property. Subsequently a family of fourth-order recurrences that share the Laurent property are considered, which are equivalent to Poisson maps in four dimensions. Two of these maps turn out to be superintegrable, and their iteration furnishes infinitely many solutions of some associated quartic Diophantine equations.
|
| first_indexed | 2025-12-07T19:20:40Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147785 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T19:20:40Z |
| publishDate | 2007 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Hone, A.N.W. 2019-02-16T08:09:10Z 2019-02-16T08:09:10Z 2007 Laurent Polynomials and Superintegrable Maps / A.N.W. Hone // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 68 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 11B37; 33E05; 37J35 https://nasplib.isofts.kiev.ua/handle/123456789/147785 This article is dedicated to the memory of Vadim Kuznetsov, and begins with some of the author's recollections of him. Thereafter, a brief review of Somos sequences is provided, with particular focus being made on the integrable structure of Somos-4 recurrences, and on the Laurent property. Subsequently a family of fourth-order recurrences that share the Laurent property are considered, which are equivalent to Poisson maps in four dimensions. Two of these maps turn out to be superintegrable, and their iteration furnishes infinitely many solutions of some associated quartic Diophantine equations. This paper is a contribution to the Vadim Kuznetsov Memorial Issue “Integrable Systems and Related Topics”. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Laurent Polynomials and Superintegrable Maps Article published earlier |
| spellingShingle | Laurent Polynomials and Superintegrable Maps Hone, A.N.W. |
| title | Laurent Polynomials and Superintegrable Maps |
| title_full | Laurent Polynomials and Superintegrable Maps |
| title_fullStr | Laurent Polynomials and Superintegrable Maps |
| title_full_unstemmed | Laurent Polynomials and Superintegrable Maps |
| title_short | Laurent Polynomials and Superintegrable Maps |
| title_sort | laurent polynomials and superintegrable maps |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147785 |
| work_keys_str_mv | AT honeanw laurentpolynomialsandsuperintegrablemaps |