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

Francesco Fassò ; Andrea Giacobbe

Symmetry, integrability and geometry: methods and applications, Tome 3 (2007)

Résumé

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.

Détail

Keywords: systems with symmetry; reconstruction; integrable systems; nonholonomic systems.

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