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Geometry of Invariant Tori of Certain Integrable Systems with Symmetry and an Application to a Nonholonomic System
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2007, том 3
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Geometry of Invariant Tori of Certain Integrable Systems with Symmetry and an Application to a Nonholonomic System
Інший ID:
2000 Mathematics Subject Classification: 37J35; 70H33
Посилання:
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.
Підтримка:
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.
Дата:
2007
Переглядів:
468
Завантажень:
187
Анотація:
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.
