The dynamics of a quasiperiodic map is analysed both in the presence and in the absence of weak noise. it is shown that, in the presence of weak noise, a strange chaotic attractor with a negative Lyapunov exponent and sensitive dependence on initial conditions can exist in the system. This means that the type of motion of a fluctuating system cannot be classified only by the sign of the leading Lyapunov exponent.
First published in Russian. In the transliteration back into English, PVEMcC's initials were corrupted.