We construct a countable family of open intervals contained in (0,1] whose endpoints are quadratic surds and such that their union is a full measure set. We then show that these intervals are precisely the monotonicity intervals of the entropy of continued fractions, thus proving a conjecture of Nakada and Natsui. © Copyright Cambridge University Press 2011.
A canonical thickening of Q and the entropy of α-continued fraction transformations / Carminati, C.; Tiozzo, G.. - In: ERGODIC THEORY & DYNAMICAL SYSTEMS. - ISSN 0143-3857. - 32:4(2012), pp. 1249-1269. [10.1017/S0143385711000447]
A canonical thickening of Q and the entropy of α-continued fraction transformations
Tiozzo G.
2012
Abstract
We construct a countable family of open intervals contained in (0,1] whose endpoints are quadratic surds and such that their union is a full measure set. We then show that these intervals are precisely the monotonicity intervals of the entropy of continued fractions, thus proving a conjecture of Nakada and Natsui. © Copyright Cambridge University Press 2011.File allegati a questo prodotto
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