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

Francesco Fassò·Andrea Giacobbe
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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.

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Francesco Fassò, Andrea Giacobbe. 2007-03-22. Geometry of Invariant Tori of Certain Integrable Systems with Symmetry and an Application to a Nonholonomic System. https://doi.org/10.3842/sigma.2007.051

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