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

作者:Carminati Carlo*; Tiozzo Giulio
来源:Ergodic Theory and Dynamical Systems, 2012, 32: 1249-1269.
DOI:10.1017/S0143385711000447

摘要

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

  • 出版日期2012-8