(2015) ETTC 2015

Proceedings ETTC 2015.zip ETTC 2015
Détails de l'article
This zip file contains all ETTC 2015 communications and the final programme
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(2015) GSI2015

Stochastic Euler-Poincaré reduction Marc Arnaudon GSI2015
Détails de l'article
We will prove a Euler-Poincaré reduction theorem for stochastic processes taking values in a Lie group, which is a generalization of the Lagrangian version of reduction and its associated variational principles. We will also show examples of its application to the rigid body and to the group of diffeomorphisms, which includes the Navier-Stokes equation on a bounded domain and the Camassa-Holm equation.
Stochastic Euler-Poincaré reduction
Actions of Lie groups and Lie algebras on symplectic and Poisson manifolds. Application to Lagrangian and Hamiltonian systems Charles-Michel Marle GSI2015
Détails de l'article
I will present some tools in Symplectic and Poisson Geometry in view of their applications in Geometric Mechanics and Mathematical Physics. Lie group and Lie algebra actions on symplectic and Poisson manifolds, momentum maps and their equivariance properties, first integrals associated to symmetries of Hamiltonian systems will be discussed. Reduction methods taking advantage of symmetries will be discussed.
Actions of Lie groups and Lie algebras on symplectic and Poisson manifolds. Application to Lagrangian and Hamiltonian systems