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arXiv · 1111.2554

Tuning and plateaux for the entropy of $α$-continued fractions

Carlo Carminati·Giulio Tiozzo
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Abstract

The entropy $h(T_α)$ of $α$-continued fraction transformations is known to be locally monotone outside a closed, totally disconnected set $\EE$. We will exploit the explicit description of the fractal structure of $\EE$ to investigate the self-similarities displayed by the graph of the function $α\mapsto h(T_α)$. Finally, we completely characterize the plateaux occurring in this graph, and classify the local monotonic behaviour.

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Carlo Carminati, Giulio Tiozzo. 2012-05-31. Tuning and plateaux for the entropy of $α$-continued fractions. https://doi.org/10.1088/0951-7715%2F26%2F4%2F1049

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