TWISTING BEHAVIOR OF CONFORMAL-MAPS

This paper is devoted to the study of different types of twisting poin ts of conformal maps, We define the sets of gyration, spiral and oscil lation points and we prove, in the case that f is conformal almost now here, that the above sets have Hausdorff dimension one. Also we define points of bounded radial oscillation. It is proved that there are alw ays points of pi-bounded radial oscillation but there exists a conform al map without points of small bounded radial oscillation.