Comments on the paper 'On a geometric theorem' by Henri Poincaré

Associated with Poincare’s “geometric theorem”, there is a number of proven and unproven propositions on fixed points of symplectic (or, as called by Poincare canonical) diffeomorphisms of symplectic manifolds more general than a circular annulus (or in an even more generally, on intersections of so-called Lagrangian submanifolds of a symplectic manifold).