On the Hausdorff dimension of the recurrent sets induced from endomorphisms of free groups
JOURNAL OF FRACTAL GEOMETRY(2022)
Abstract
We show that F. Dekking's recurrent sets in R-2, which correspond to Markov partitions for conformally expanding maps of the 2-torus, have Hausdorff dimension strictly greater than one. This is a counterpart to the classical result of R. Bowen on the non-smoothness of the Markov partitions for Anosov diffeomorphisms of the 3-torus. We also present a non-conformal example where the recurrent set is a parallelogram and hence its Hausdorff dimension is one.
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Key words
Recurrent set, Hausdorff dimension, Markov partition
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