Geometry of Invariant Tori of Certain Integrable Systems with Symmetry and an Application to a Nonholonomic System

Details Geometry of Invariant Tori of Certain Integrable Systems with Symmetry and an Application to a Nonholonomic System Geometry of Invariant Tori of Certain Integrable Systems with Symmetry and an Application to a Nonholonomic System

2007-03-22

arxiv.org/abs/math/0703665v1

SIGMA 3 (2007), 051, 12 pages

Mathematics

Symplectic Geometry

This is a contribution to the Proc. of workshop on Geometric Aspects of Integrable Systems (July 17-19, 2006; Coimbra, Portuga

Scientific paper

10.3842/SIGMA.2007.051

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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