Symplectic mechanics deals with symplectic flows. I wonder, how general this description of the possible (or imaginable) dynamical phenomena is. If a given flow on a symplectic manifold turns to be non-symplectic, then perhaps we can find another symplectic form on the manifold that is invariant to the flow, that is, this flow can remain inside the relam of symplectic mechanics. Are there flows on even dimensional orientable manifolds that don't have any invariant symplectic form? If yes, then what look they like? In other words what kind of dynamical phenomena are excluded from symplectic mchanics?