Classical and quantum dynamics in transverse geometry of Riemannian foliations

First, we survey some results on classical and quantum dynamical systems associated with transverse Dirac operators on Riemannian foliations. Then we illustrate these results by two examples of Riemannian foliations: a foliation given by the fibers of a fibration and a linear foliation on the two-dimensional torus.
Comment: 19 pages, to be published in the proceedings of the conference 'Spectrum and Dynamics', Montr\'eal, 2008