BIFURCATION TO STRANGE NONCHAOTIC ATTRACTORS

Strange nonchaotic attractors are attractors that are geometrically st range, but have nonpositive Lyapunov exponents. These attractors occur in regimes of nonzero Lebesgue measure in the parameter space of quas iperiodically driven dissipative dynamical systems. We investigate a r oute to strange nonchaotic attractors in systems with a symmetric inva riant subspace. Assuming there is a quasiperiodic torus in the invaria nt subspace, we show that the loss of the transverse stability of the tonus can lead to the birth of a strange nonchaotic attractor. A physi cal phenomenon accompanying this route to strange nonchaotic attractor s is an extreme type of intermittency. We expect this route to be phys ically observable, and we present theoretical arguments and numerical examples with both quasiperiodically driven maps and quasiperiodically driven flows. The transition to chaos from the strange nonchaotic beh avior is also studied.