Singularity confinement and algebraic integrability
Two important notions of integrability for discrete mappings are algebraic integrability and singularity confinement, have been used for discrete mappings. Algebraic integrability is related to the existence of sufficiently many conserved quantities whereas singularity confinement is associated with...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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2003
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| _version_ | 1797054779867791360 |
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| author | Lafortune, S Goriely, A |
| author_facet | Lafortune, S Goriely, A |
| author_sort | Lafortune, S |
| collection | OXFORD |
| description | Two important notions of integrability for discrete mappings are algebraic integrability and singularity confinement, have been used for discrete mappings. Algebraic integrability is related to the existence of sufficiently many conserved quantities whereas singularity confinement is associated with the local analysis of singularities. In this paper, the relationship between these two notions is explored for birational autonomous mappings. Two types of results are obtained: first, algebraically integrable mappings are shown to have the singularity confinement property. Second, a proof of the non-existence of algebraic conserved quantities of discrete systems based on the lack of confinement property is given. |
| first_indexed | 2024-03-06T19:02:03Z |
| format | Journal article |
| id | oxford-uuid:13dd5497-046a-4576-83a7-826973f3b4d1 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T19:02:03Z |
| publishDate | 2003 |
| record_format | dspace |
| spelling | oxford-uuid:13dd5497-046a-4576-83a7-826973f3b4d12022-03-26T10:16:16ZSingularity confinement and algebraic integrabilityJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:13dd5497-046a-4576-83a7-826973f3b4d1EnglishSymplectic Elements at Oxford2003Lafortune, SGoriely, ATwo important notions of integrability for discrete mappings are algebraic integrability and singularity confinement, have been used for discrete mappings. Algebraic integrability is related to the existence of sufficiently many conserved quantities whereas singularity confinement is associated with the local analysis of singularities. In this paper, the relationship between these two notions is explored for birational autonomous mappings. Two types of results are obtained: first, algebraically integrable mappings are shown to have the singularity confinement property. Second, a proof of the non-existence of algebraic conserved quantities of discrete systems based on the lack of confinement property is given. |
| spellingShingle | Lafortune, S Goriely, A Singularity confinement and algebraic integrability |
| title | Singularity confinement and algebraic integrability |
| title_full | Singularity confinement and algebraic integrability |
| title_fullStr | Singularity confinement and algebraic integrability |
| title_full_unstemmed | Singularity confinement and algebraic integrability |
| title_short | Singularity confinement and algebraic integrability |
| title_sort | singularity confinement and algebraic integrability |
| work_keys_str_mv | AT lafortunes singularityconfinementandalgebraicintegrability AT gorielya singularityconfinementandalgebraicintegrability |