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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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National Academy of Science of Ukraine
2007-03-01
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Subjects: | |
| Online Access: | http://www.emis.de/journals/SIGMA/2007/051/ |
| _version_ | 1819142694008520704 |
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| author | Francesco Fassò Andrea Giacobbe |
| author_facet | Francesco Fassò Andrea Giacobbe |
| author_sort | Francesco Fassò |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-12-22T12:14:25Z |
| format | Article |
| id | doaj.art-62ce56a3739d4833afdd6fa9f7a3673b |
| institution | Directory Open Access Journal |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2024-12-22T12:14:25Z |
| publishDate | 2007-03-01 |
| publisher | National Academy of Science of Ukraine |
| record_format | Article |
| series | Symmetry, Integrability and Geometry: Methods and Applications |
| spelling | doaj.art-62ce56a3739d4833afdd6fa9f7a3673b2022-12-21T18:26:11ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592007-03-013051Geometry of Invariant Tori of Certain Integrable Systems with Symmetry and an Application to a Nonholonomic SystemFrancesco FassòAndrea GiacobbeBifibrations, 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.http://www.emis.de/journals/SIGMA/2007/051/systems with symmetryreconstructionintegrable systemsnonholonomic systems |
| spellingShingle | Francesco Fassò Andrea Giacobbe Geometry of Invariant Tori of Certain Integrable Systems with Symmetry and an Application to a Nonholonomic System Symmetry, Integrability and Geometry: Methods and Applications systems with symmetry reconstruction integrable systems nonholonomic systems |
| title | 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_short | 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 |
| topic | systems with symmetry reconstruction integrable systems nonholonomic systems |
| url | http://www.emis.de/journals/SIGMA/2007/051/ |
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