Chaotic sets and Hausdorff dimension for L\"uroth expansions
Rafael Alcaraz Barrera, Gerardo Gonz\'alez Robert
TL;DR
This paper explores the similarities between L"uroth expansions and continued fractions, focusing on their topological dynamics and Hausdorff dimension, and provides analogues of known results for the Gauss map.
Contribution
It establishes a complete analogue for the L"uroth transformation of results related to pairs in the Gauss map, highlighting new connections in dynamical systems.
Findings
Identifies similarities between L"uroth series and continued fractions.
Establishes Hausdorff dimension results for L"uroth expansions.
Provides analogues of known Gauss map properties for L"uroth transformations.
Abstract
We provide new similarities between regular continued fractions and L\"uroth series in terms of topological dynamics and Hausdorff dimension. In particular, we establish a complete analogue for the L\"uroth 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.
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