Chaotic sets and Hausdorff dimension for Lüroth expansions
Abstract
We provide new similarities between regular continued fractions and Lüroth series in terms of topological dynamics and Hausdorff dimension. In particular, we establish a complete analogue for the Lüroth transformation of results by W. Liu, B. Li and W. Liu, S. Wang on the distal, asymptotic and Li-Yorke pairs for the Gauss map.
- Publication:
-
arXiv e-prints
- Pub Date:
- December 2021
- DOI:
- 10.48550/arXiv.2112.04714
- arXiv:
- arXiv:2112.04714
- Bibcode:
- 2021arXiv211204714A
- Keywords:
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- Mathematics - Dynamical Systems;
- Mathematics - Number Theory;
- 11K55;
- 37B10;
- 11K55;
- 11J70
- E-Print:
- 27 pages