Smooth shifts along flows

الأصل · EN

Let Φ be a flow on a smooth, compact, finite-dimensional manifold M. Consider the subsets E(Φ) and D(Φ) of C∞(M,M) consisting of smoothh mappings and diffeomorphisms (respectively) of M preserving the foliation of the flow Φ. Let also E₀(Φ) and D₀(Φ) be the identity path components of E(Φ) and D(Φ) with compact-open topology. We prove that under mild conditions on fixed points of Φ the inclusion D₀(Φ) ⊂ E₀(Φ) is a homotopy equivalence and these spaces are either contractible or homotopically equivalent to the circle.