| 研究実績の概要 |
This was a very successful project.A complete multifractal analysis of the cusp windings spectrum for essentially free Fuchsian groups with parabolic elements has been obtained. These results have been submitted for publication (joint work with Marc Kesseboehmer (University Bremen, Germany) and Sara Munday (University of Bologna, Italy).New results have been obtained for the amenability of skew product extensions of topological Markov chains by infinite groups and graphs (joint with M Stadlbauer). Related results (with K Matsuzaki) have been accepted for publication in Proceedings of the American Mathematical Society. The revision of the analysis of complex Takagi functions (joint with H Sumi) has been completed. For Takagi functions associated with interval maps satisfying the open set condition we found that a.e. properties of the pointwise Hoelder exponent can be obtained from the ergodic theorem.The previous paper on non-hyperbolic and infinitely generated rational semigroups (joint with H Sumi, to appear in Transactions of the American Mathematical Society) is now in print.
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