Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 3 (2007), 051, 12 pages      math.SG/0703665
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

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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