Completely Integrable Contact Hamiltonian Systems and Toric Contact Structures on S²×S³
I begin by giving a general discussion of completely integrable Hamiltonian systems in the setting of contact geometry. We then pass to the particular case of toric contact structures on the manifold S²×S³. In particular we give a complete solution to the contact equivalence problem for a class of t...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2011 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2011
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147180 |
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| Cite this: | Completely Integrable Contact Hamiltonian Systems and Toric Contact Structures on S²×S³ / C.P. Boyer // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 58 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-147180 |
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Boyer, C.P. 2019-02-13T18:32:17Z 2019-02-13T18:32:17Z 2011 Completely Integrable Contact Hamiltonian Systems and Toric Contact Structures on S²×S³ / C.P. Boyer // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 58 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 53D42; 53C25 DOI:10.3842/SIGMA.2011.058 https://nasplib.isofts.kiev.ua/handle/123456789/147180 I begin by giving a general discussion of completely integrable Hamiltonian systems in the setting of contact geometry. We then pass to the particular case of toric contact structures on the manifold S²×S³. In particular we give a complete solution to the contact equivalence problem for a class of toric contact structures, Yp,q, discovered by physicists by showing that Yp,q and Yp',q' are inequivalent as contact structures if and only if p≠p'. This paper is a contribution to the Special Issue “Symmetry, Separation, Super-integrability and Special Functions (S⁴)”. The full collection is available at http://www.emis.de/journals/SIGMA/S4.html. During the conference I enjoyed conversations with E. Kalnins, N. Kamran, J. Kress, W. Miller Jr., and P. Winternitz. I also want to thank J. Pati, my collaborator in [25] without whom the present paper could not have been written. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Completely Integrable Contact Hamiltonian Systems and Toric Contact Structures on S²×S³ Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Completely Integrable Contact Hamiltonian Systems and Toric Contact Structures on S²×S³ |
| spellingShingle |
Completely Integrable Contact Hamiltonian Systems and Toric Contact Structures on S²×S³ Boyer, C.P. |
| title_short |
Completely Integrable Contact Hamiltonian Systems and Toric Contact Structures on S²×S³ |
| title_full |
Completely Integrable Contact Hamiltonian Systems and Toric Contact Structures on S²×S³ |
| title_fullStr |
Completely Integrable Contact Hamiltonian Systems and Toric Contact Structures on S²×S³ |
| title_full_unstemmed |
Completely Integrable Contact Hamiltonian Systems and Toric Contact Structures on S²×S³ |
| title_sort |
completely integrable contact hamiltonian systems and toric contact structures on s²×s³ |
| author |
Boyer, C.P. |
| author_facet |
Boyer, C.P. |
| publishDate |
2011 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
I begin by giving a general discussion of completely integrable Hamiltonian systems in the setting of contact geometry. We then pass to the particular case of toric contact structures on the manifold S²×S³. In particular we give a complete solution to the contact equivalence problem for a class of toric contact structures, Yp,q, discovered by physicists by showing that Yp,q and Yp',q' are inequivalent as contact structures if and only if p≠p'.
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| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/147180 |
| citation_txt |
Completely Integrable Contact Hamiltonian Systems and Toric Contact Structures on S²×S³ / C.P. Boyer // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 58 назв. — англ. |
| work_keys_str_mv |
AT boyercp completelyintegrablecontacthamiltoniansystemsandtoriccontactstructuresons2s3 |
| first_indexed |
2025-12-07T18:44:37Z |
| last_indexed |
2025-12-07T18:44:37Z |
| _version_ |
1850876181920874496 |