A canonical thickening of ℚ and the entropy ofα-continued fraction transformations-Reference-Cited by-同舟云学术

A canonical thickening of ℚ and the entropy ofα-continued fraction transformations

Published:2011-09-14 Issue:4 Volume:32 Page:1249-1269
ISSN:0143-3857
Container-title:Ergodic Theory and Dynamical Systems
language:en
Short-container-title:Ergod. Th. Dynam. Sys.

Author:

CARMINATI CARLO,TIOZZO GIULIO

Abstract

AbstractWe 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 ofα-continued fractions, thus proving a conjecture of Nakada and Natsui.

Publisher

Cambridge University Press (CUP)

Subject

Applied Mathematics,General Mathematics

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