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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...
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Інститут математики НАН України
2007
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/147785 |
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irk-123456789-1477852019-02-17T01:26:39Z Laurent Polynomials and Superintegrable Maps Hone, A.N.W. 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. 2007 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/147785 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Hone, A.N.W. |
| spellingShingle |
Hone, A.N.W. Laurent Polynomials and Superintegrable Maps Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Hone, A.N.W. |
| author_sort |
Hone, A.N.W. |
| title |
Laurent Polynomials and Superintegrable Maps |
| title_short |
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_sort |
laurent polynomials and superintegrable maps |
| publisher |
Інститут математики НАН України |
| publishDate |
2007 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147785 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT honeanw laurentpolynomialsandsuperintegrablemaps |
| first_indexed |
2023-05-20T17:28:31Z |
| last_indexed |
2023-05-20T17:28:31Z |
| _version_ |
1796153383296434176 |