ИСТИНА

By a gradient-like flow on a closed orientable surface S, we mean a closed 1-form b defined on S punctured at a finite set of points (sources and sinks of b) such that there exists a Morse function f on S, called an energy function of b, whose critical points coincide with equilibria of b, and the pair (f,b) has a canonical form near each critical point of f. Let B=B(b_0) be the space of all gradient-like flows on S having the same types of local singularities as a flow b_0, and F=F(f_0) the space of all Morse functions on S having the same types of local singularities as an energy function f_0 of b_0. We prove that the spaces F and B, equipped with C^\infty topologies, are homotopy equivalent to some manifold M_s, moreover their decompositions into Diff^0(S)-orbits are given by two transversal fibrations on M_s. Similar results are proved for topological equivalence classes on F and B, and for non-Morse singularities.