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Journal of the London Mathematical Society 1997 56(1):16-36; doi:10.1112/S0024610797005334
© 1997 by London Mathematical Society
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© The London Mathematical Society

Twisting Behaviour of Conformal Maps

Joan Josep Carmona and Christian Pommerenke

Departament de Matemàtiques, Universitat Autònoma de Barcelona 08193 Bellaterra (Barcelona), Spain
Technische Universität Fachbereich Mathematik, 10623 Berlin, Germany

Received 28 June 1994. Revision received 16 June 1995.

This paper is devoted to the study of different types of twisting points of conformal maps. We define the sets of gyration, spiral and oscillation points and we prove, in the case that f is conformal almost nowhere, that the above sets have Hausdorff dimension one. Also we define points of bounded radial oscillation. It is proved that there are always points of {pi}-bounded radial oscillation but there exists a conformal map without points of small bounded radial oscillation.


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