Degeneration from difference to differential Okamoto spaces for the sixth Painlevé equation
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866929550486667264 |
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| author | Dreyfus, Thomas Heu, Viktoria |
| author_facet | Dreyfus, Thomas Heu, Viktoria |
| contents | In the current paper we study the $q$-analogue introduced by Jimbo and Sakai of the well known Painlevé VI differential equation. We explain how it can be deduced from a $q$-analogue of Schlesinger equations and show that for a convenient change of variables and auxiliary parameters, it admits a $q$-analogue of Hamiltonian formulation. This allows us to show that Sakai's $q$-analogue of Okamoto space of initial conditions for $qP_\mathrm{VI}$ admits the differential Okamoto space \emph{via} some natural limit process. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2005_12805 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Degeneration from difference to differential Okamoto spaces for the sixth Painlevé equation Dreyfus, Thomas Heu, Viktoria Classical Analysis and ODEs 14D05, 14F35, 34M56, 39A13 In the current paper we study the $q$-analogue introduced by Jimbo and Sakai of the well known Painlevé VI differential equation. We explain how it can be deduced from a $q$-analogue of Schlesinger equations and show that for a convenient change of variables and auxiliary parameters, it admits a $q$-analogue of Hamiltonian formulation. This allows us to show that Sakai's $q$-analogue of Okamoto space of initial conditions for $qP_\mathrm{VI}$ admits the differential Okamoto space \emph{via} some natural limit process. |
| title | Degeneration from difference to differential Okamoto spaces for the sixth Painlevé equation |
| topic | Classical Analysis and ODEs 14D05, 14F35, 34M56, 39A13 |
| url | https://arxiv.org/abs/2005.12805 |