Reduced dynamics and Lagrangian submanifolds of symplectic manifolds
  In this paper, we will see that the symplectic creed by Weinstein "everything is a Lagrangian submanifold" also holds for Hamilton-Poincar\'e and Lagrange-Poincar\'e reduction. In fact, we show that solutions of the Hamilton-Poincar\'e equations and of the Lagrange-Poincar\'e equations are in one-to-one correspondence with distinguished curves in a Lagrangian submanifold of a symplectic manifold. For this purpose, we will combine the concept of a Tulczyjew triple with Marsden-Weinstein symplectic reduction. 
E. Garc\'ia-Tora\~no Andr\'es, E. Guzm\'an, J.C. Marrero, T. Mestdag
math.DG math-ph math.MP