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

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

#### Abstract

The entropy h(Tα) of α-continued fraction transformations is known to be locally monotone outside a closed, totally disconnected set $\mathcal{E}$ . We will exploit the explicit description of the fractal structure of $\mathcal{E}$ to investigate the self-similarities displayed by the graph of the function α map h(Tα). Finally, we completely characterize the plateaux occurring in this graph, and classify the local monotonic behaviour.
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Carminati, Carlo; Tiozzo, G.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11568/208731
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