Let Φ be a flow on a smooth, compact, finite-dimensional manifold M . Consider the subset D(Φ) of C ∞ (M, M ) consisting of diffeomorphisms of M preserving the foliation of the flow Φ. Let also D 0 (Φ) be the identity path component of D(Φ) with compactopen topology. We prove that under mild conditions on fixed points of Φ the space D 0 (Φ) is either contractible or homotopically equivalent to S 1 .
Let f : T 2 → R be a Morse function on a 2-torus, S(f ) and O(f ) be its stabilizer and orbit with respect to the right action of the group D(T 2 ) of diffeomorphisms of T 2 , D id (T 2 ) be the identity path component of D(T 2 ), andIn fact this result holds for a larger class of smooth functions f : T 2 → R having the following property: for every critical point z of f the germ of f at z is smothly equivalent to a homogeneous polynomial R 2 → R without multiple factors.2000 Mathematics Subject Classification. 57S05, 57R45, 37C05.
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