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On the Hausdorff dimension of a set of complex continued fractions

1983
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Illinois Journal of Mathematics
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This note arose from some general considerations concerning geometric representations of the shift operator. Specifically, consider an infinite set T, the product space TN, and shift operator S T N --> T defined by S(<tl, t2, t3, ...) <t2, t3 . One can ask whether there are some natural measures on T N with respect to which S is ergodic or mixing. From our point of view the answer depends on the geometric structure of a representation of this space. For example, if T N, then there are, of

doi:10.1215/ijm/1256046498
fatcat:37mwyjlstvhbzmk2tusvnlr6ki