Maksymenko S. Deformations along orbits of flows and their applications

The thesis is devoted to study of smooth maps which leave invariant orbits of flows on manifolds. It is proved that for a large class of vector fields on compact manifolds to prove contractibility of path components of diffeomorphisms groups preserving orbits of such vector fields. For a large class of smooth functions with isolated singularities of compact surfaces we calculated the homotopy types of right stabilizers and right orbits. Also it is obtained a new proof of the classification of the path components space of Morse maps from compact surfaces to the real line and to the circle.