Saratov State University, Russia

We investigate the well-known system with period-doublings – Ikeda map – driven by the signal with incommensurate frequency at different dissipation levels including very small ones. The work consists of two parts. One deals with the number and structure of coexisting attractors for different dissipation levels in comparison with the map without driving signal. Other is the search for the strange nonchaotic attractor which are known to be typical for quasiperiodically driven maps and its transformation with the decrease of dissipation level.