Vendredi 16 Janvier 2015

11h: Paula BALSEIRO (Rio)
Nonholonomic systems and the hamiltonization problem

Abstract : In this talk we will discuss geometric features of nonholonomic systems and their behaviour after a reduction by a group of symmetries. We will see how Poisson geometry helps in understanding how far these systems are from being hamiltonian. In particular, we will show how the failure of the Jacobi identity is modified after a reduction by symmetries and we will present some concrete examples where Poisson and twisted Poisson brackets appear in the description of the dynamics. Moreover, in these cases, it is be possible to obtain a complete description of the (almost) symplectic leaves associated to these brackets.

References :

[1] P. Balseiro, The Jacobiator of nonholonomic systems and the geometry of reduced non- holonomic brackets. Archive for Rational Mechanics and Analysis. 214(2) (2014), 453-501.

[2] P. Balseiro, L. Garcia-Naranjo, Gauge Transformations, Twisted Poisson Brackets and Hamiltonization of Nonholonomic Systems, Archive for Rational Mechanics and Analysis,
205, 1 (2012), 267-310.

[3] P. Balseiro, O. Fernandez, Nonholonomic reduction in two steps, Preprint.

Vendredi 23 Janvier 2015

11h: Michaël PEVZNER (Reims)
Quantification covariante et brisure des symétries