Scaling of Fractal Basin Boundaries near Intermittency Transitions to Chaos

It is the purpose of this paper to point out that the creation of fractal basin boundaries is a characteristic feature accompanying the intermittency transition to chaos. (Here ‘‘intermittency’’ transition is used in the sense of Pomeau and Manneville [Commun. Math. Phys. 74, 189 (1980)]; viz., a chaotic attractor is created as a periodic orbit becomes unstable.) In particular, we are here concerned with type-I and type-III intermittencies. We examine the scaling of the dimension of basin boundaries near these intermittency transitions.