Budnytska T. A topological conjugacy of maps.

This dissertation is devoted to topological classification of maps. In particular, we obtain the results on classification of linear and affine maps and linear fractional transformations up to topological conjugacy. We give criteria of topological conjugacy of an affine map with its corresponding linear map, which admits to classify the some affine maps using only their linear parts. Furthermore, the topological classifications of a large class of real and complex affine maps and all affine maps that act on the field of quaternions are obtained. Finally, the necessary and sufficient conditions for topological conjugacy of linear fractional transformations in terms of their fixed points and matrices are formulated. We describe the classes of topological conjugate linear fractional transformations by using the classification of these transformations by their standart's forms.