THE BIRTH OF STRANGE NONCHAOTIC ATTRACTORS

A mechanism is described for the development of strange nonchaotic att ractors from two-frequency quasiperiodic attractors in quasiperiodical ly driven maps. This mechanism is intimately tied to the phenomenon of torus-doubling. The transition to strange nonchaotic behavior occurs when a period-doubled torus collides with its unstable parent torus. A s the collision is approached, the period-doubled torus becomes extrem ely wrinkled, ultimately becoming fractal at the collision. The Lyapun ov exponent remains negative through the collision. These collisions a re shown to be a new type of attractor merging crisis; the new feature is the possibility of nonchaotic attractors taking part in the crisis . This mechanism is illustrated via numerical and analytical studies o f a quasiperiodically driven logistic map.