4 1. INTRODUCTIO N

FIGURE

1.2. Fatou-Bieberbac h Domai n

iii.- Th e periodi c orbit s o f F ar e dens e i n K .

It turn s ou t tha t i n dimensions abov e 1, the ma p F i s not chaoti c on the whol e

Julia set . Fo r thi s reaso n i t i s mor e natura l t o stud y th e nonwanderin g par t o f

the Juli a set . Suppos e tha t F i s a continuou s self-ma p o f some manifol d M . The n

a poin t p G M i s nonwandering i f given an y neighborhoo d U of p G M, ther e i s a n

integer n 1 so that f

n(U)

D U ^ 0 . I f not , p i s wandering. Se e figure 1.5.