Non-Integrability of the Sasano System of Type ⁽¹⁾₅ and Stokes Phenomena
In 2006, Y. Sasano proposed higher-order Painlevé systems, which admit affine Weyl group symmetry of type ⁽¹⁾ₗ, = 4, 5, 6, …. In this paper, we study the integrability of a four-dimensional Painlevé system, which has symmetry under the extended affine Weyl group ˜(⁽¹⁾₅) and which we call the Sasano...
Saved in:
| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2025 |
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2025
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/212871 |
| 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: | Non-Integrability of the Sasano System of Type ⁽¹⁾₅ and Stokes Phenomena. Tsvetana Stoyanova. SIGMA 21 (2025), 020, 24 pages |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862618971901001728 |
|---|---|
| author | Stoyanova, Tsvetana |
| author_facet | Stoyanova, Tsvetana |
| citation_txt | Non-Integrability of the Sasano System of Type ⁽¹⁾₅ and Stokes Phenomena. Tsvetana Stoyanova. SIGMA 21 (2025), 020, 24 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | In 2006, Y. Sasano proposed higher-order Painlevé systems, which admit affine Weyl group symmetry of type ⁽¹⁾ₗ, = 4, 5, 6, …. In this paper, we study the integrability of a four-dimensional Painlevé system, which has symmetry under the extended affine Weyl group ˜(⁽¹⁾₅) and which we call the Sasano system of type ⁽¹⁾₅. We prove that one family of the Sasano system of type ⁽¹⁾₅ is not integrable by rational first integrals. We describe Stokes phenomena relative to a subsystem of the second normal variational equations. This approach allows us to compute in an explicit way the corresponding differential Galois group and therefore to determine whether the connected component of its unit element is not Abelian. Applying the Morales-Ramis-Simó theory, we establish a non-integrable result.
|
| first_indexed | 2026-03-21T11:56:45Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212871 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-21T11:56:45Z |
| publishDate | 2025 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Stoyanova, Tsvetana 2026-02-13T13:48:53Z 2025 Non-Integrability of the Sasano System of Type ⁽¹⁾₅ and Stokes Phenomena. Tsvetana Stoyanova. SIGMA 21 (2025), 020, 24 pages 1815-0659 2020 Mathematics Subject Classification: 34M55; 37J30; 34M40; 37J65 arXiv:2306.07062 https://nasplib.isofts.kiev.ua/handle/123456789/212871 https://doi.org/10.3842/SIGMA.2025.020 In 2006, Y. Sasano proposed higher-order Painlevé systems, which admit affine Weyl group symmetry of type ⁽¹⁾ₗ, = 4, 5, 6, …. In this paper, we study the integrability of a four-dimensional Painlevé system, which has symmetry under the extended affine Weyl group ˜(⁽¹⁾₅) and which we call the Sasano system of type ⁽¹⁾₅. We prove that one family of the Sasano system of type ⁽¹⁾₅ is not integrable by rational first integrals. We describe Stokes phenomena relative to a subsystem of the second normal variational equations. This approach allows us to compute in an explicit way the corresponding differential Galois group and therefore to determine whether the connected component of its unit element is not Abelian. Applying the Morales-Ramis-Simó theory, we establish a non-integrable result. The author is indebted to the referees for their critical remarks and advice towards the improvement of the paper. The author was partially supported by Grant KP-06-N 62/5 of the Bulgarian Fund “Scientific research”. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Non-Integrability of the Sasano System of Type ⁽¹⁾₅ and Stokes Phenomena Article published earlier |
| spellingShingle | Non-Integrability of the Sasano System of Type ⁽¹⁾₅ and Stokes Phenomena Stoyanova, Tsvetana |
| title | Non-Integrability of the Sasano System of Type ⁽¹⁾₅ and Stokes Phenomena |
| title_full | Non-Integrability of the Sasano System of Type ⁽¹⁾₅ and Stokes Phenomena |
| title_fullStr | Non-Integrability of the Sasano System of Type ⁽¹⁾₅ and Stokes Phenomena |
| title_full_unstemmed | Non-Integrability of the Sasano System of Type ⁽¹⁾₅ and Stokes Phenomena |
| title_short | Non-Integrability of the Sasano System of Type ⁽¹⁾₅ and Stokes Phenomena |
| title_sort | non-integrability of the sasano system of type ⁽¹⁾₅ and stokes phenomena |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212871 |
| work_keys_str_mv | AT stoyanovatsvetana nonintegrabilityofthesasanosystemoftype15andstokesphenomena |