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SIGMA 3 (2007), 051, 12 pages math.SG/0703665
https://doi.org/10.3842/SIGMA.2007.051
Contribution to the Proceedings of the Coimbra Workshop on
Geometric Aspects of Integrable Systems
Geometry of Invariant Tori of Certain Integrable Systems with Symmetry and an Application to a Nonholonomic System
Francesco Fassò and Andrea Giacobbe
Dipartimento di Matematica Pura e Applicata, Università di Padova,
Via Trieste 63, 35131 Padova, Italy
Received November 20, 2006, in final form March 15, 2007; Published online March 22, 2007
Abstract
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.
Key words:
systems with symmetry; reconstruction; integrable systems; nonholonomic systems.
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