On the Conley index in the invariant manifolds

Let ϕϕ be a flow on a manifold MM and assume that N⊂MN⊂M is an invariant manifold. The aim of this note is to compare the Conley indices of an isolated invariant set S⊂NS⊂N with respect to the flow ϕϕ and the flow ϕϕ restricted to NN.