Global center manifolds in singular systems

The problem of existence of a global center manifold for a system of O.D.E. like { x(over dot) = A(y)x + F(x, y) y(over dot) = G(x, y), (x, y) is an element of R-n x R-m (*) is considered. We give conditions on A(y), F(x, y), G(x, y) in order that a function H : R-m -> R-n, with the same smoothness as A(y), F(x, y), G(x, y), exists and is such that the manifold C = {(x, y) is an element of R-n x R-m vertical bar x = H(y), y is an element of R-m} is an invariant manifold for (*), and there exists rho > 0 such that any solution of (*) satisfying sup(t is an element of R)vertical bar x(t)vertical bar < rho must belong to C. This is why we call C global center manifold. Applications are given to the problem of existence of heteroclinic orbits in singular systems.