Symmetries and Lagrangian time-discretizations of Euler equations Alexei Penskoi (penskoi@crm.umontreal.ca) Abstract In late 80s - early
90s J. Moser and A. P. Veselov considered Lagrangian discrete systems
on Lie groups with additional symmetry conditions imposed on Lagrangians.
They observed that such systems are often integrable time-discretizations
of integrable Euler equations on these Lie groups. In recent papers we
studied Lagrangian discrete systems with additional symmetry requirements
on certain infinite-dimensional Lie groups. We will discuss some interesting
properties of these systems. |