Topological conjugation of nonsingular surface flows

For today topological classifcation in sense of topological equiv- alence is obtained for Morse-Smale flows completely, and also for their generalisation Ω-stable flows on closed surfaces. Some results on topological conjugacy classification for such systems are also known. Thus, there is found that topological eqiuvalence and topological con- jugacy classes coincide for gradient-like flows (i.e. Morse-Smale flows with- out periodic orbits). In the classical work there is proved that existence of the connections (the case of coincidence of saddle separatrices) decom- poses a topological equivalence class of an Ω-stable flows into continuum topological conjugacy classes (i.e. a flow has moduli). Obvious that each periodic orbit also generates at least one modulus related with the orbit's period. In this work there is found that the cell bounded by the limit cycles leads to infinite number of moduli of stability. Besides, there is found the criterion of topological conjugacy of flows in such cells.