Quantitative mixing results and inner functions

19 pages, no figures.-- MSC2000 codes: 30D05, 30D50, 37A05, 37A25, 37F10, 28D05, 11K55.MR#: MR2262783 (2007j:37003)Zbl#: Zbl 1125.30019We study in this paper estimates on the size of the sets of points which are well approximated by orbits of other points under certain dynamical systems. We apply the results obtained to the particular case of the dynamical system generated by inner functions in the unit disk of the complex plane.D. Pestana was supported by Grants BFM2003-04780 and BFM-2003-06335-C03-02, Ministerio de Ciencia y Tecnología, Spain. J. L. Fernández and M. V. Melián were supported by Grant BFM2003-04780 from Ministerio de Ciencia y Tecnología, Spain.Publicad