  We consider a scenario when a stable and unstable manifolds of compact center
manifold of a saddle-center coincide. The normal form of the ODE governing the
system near the center manifold is derived and so is the normal form of the
return map to the neighbourhood of the center manifold. The limit dynamics of
the return map is investigated by showing that it might take the form of a
Henon-like map possessing a Lorenz-like attractor or satisfy 'cone-field
condition' resulting in partial hyperbolicity. We consider also motivating
example from game theory.
