Geometry of Invariant Tori of Certain Integrable Systems with Symmetry and an Application to a Nonholonomic System
Bifibrations, in symplectic geometry called also dual pairs, play a relevant role in the theory of superintegrable Hamiltonian systems. We prove the existence of an analogous bifibrated geometry in dynamical systems with a symmetry group such that the reduced dynamics is periodic. The integrability...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2007 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2007
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/147810 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Geometry of Invariant Tori of Certain Integrable Systems with Symmetry and an Application to a Nonholonomic System / F. Fassò, A. Giacobbe // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 20 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-147810 |
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Fassò, F. Giacobbe, A. 2019-02-16T08:37:14Z 2019-02-16T08:37:14Z 2007 Geometry of Invariant Tori of Certain Integrable Systems with Symmetry and an Application to a Nonholonomic System / F. Fassò, A. Giacobbe // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 20 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 37J35; 70H33 https://nasplib.isofts.kiev.ua/handle/123456789/147810 Bifibrations, in symplectic geometry called also dual pairs, play a relevant role in the theory of superintegrable Hamiltonian systems. We prove the existence of an analogous bifibrated geometry in dynamical systems with a symmetry group such that the reduced dynamics is periodic. The integrability of such systems has been proven by M. Field and J. Hermans with a reconstruction technique. We apply the result to the nonholonomic system of a ball rolling on a surface of revolution. This paper is a contribution to the Proceedings of the Workshop on Geometric Aspects of Integrable Systems (July 17–19, 2006, University of Coimbra, Portugal). The authors thank the Bernoulli Center (EPFL, Lausanne) for its hospitality during the 2004 program Geometric Mechanics and Its Applications, where the biggest part of this work was done, and Hans Duistermaat for some enlightening conversations on these topics. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Geometry of Invariant Tori of Certain Integrable Systems with Symmetry and an Application to a Nonholonomic System Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Geometry of Invariant Tori of Certain Integrable Systems with Symmetry and an Application to a Nonholonomic System |
| spellingShingle |
Geometry of Invariant Tori of Certain Integrable Systems with Symmetry and an Application to a Nonholonomic System Fassò, F. Giacobbe, A. |
| title_short |
Geometry of Invariant Tori of Certain Integrable Systems with Symmetry and an Application to a Nonholonomic System |
| title_full |
Geometry of Invariant Tori of Certain Integrable Systems with Symmetry and an Application to a Nonholonomic System |
| title_fullStr |
Geometry of Invariant Tori of Certain Integrable Systems with Symmetry and an Application to a Nonholonomic System |
| title_full_unstemmed |
Geometry of Invariant Tori of Certain Integrable Systems with Symmetry and an Application to a Nonholonomic System |
| title_sort |
geometry of invariant tori of certain integrable systems with symmetry and an application to a nonholonomic system |
| author |
Fassò, F. Giacobbe, A. |
| author_facet |
Fassò, F. Giacobbe, A. |
| publishDate |
2007 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
Bifibrations, in symplectic geometry called also dual pairs, play a relevant role in the theory of superintegrable Hamiltonian systems. We prove the existence of an analogous bifibrated geometry in dynamical systems with a symmetry group such that the reduced dynamics is periodic. The integrability of such systems has been proven by M. Field and J. Hermans with a reconstruction technique. We apply the result to the nonholonomic system of a ball rolling on a surface of revolution.
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| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/147810 |
| citation_txt |
Geometry of Invariant Tori of Certain Integrable Systems with Symmetry and an Application to a Nonholonomic System / F. Fassò, A. Giacobbe // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 20 назв. — англ. |
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AT fassof geometryofinvarianttoriofcertainintegrablesystemswithsymmetryandanapplicationtoanonholonomicsystem AT giacobbea geometryofinvarianttoriofcertainintegrablesystemswithsymmetryandanapplicationtoanonholonomicsystem |
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2025-12-07T17:11:44Z |
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2025-12-07T17:11:44Z |
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1850870338084143104 |