Displaying similar documents to “Entropies of the partitions of the unit interval generated by the Farey tree”

Orderings of the rationals and dynamical systems

Claudio Bonanno, Stefano Isola (2009)

Colloquium Mathematicae

Similarity:

This paper is devoted to a systematic study of a class of binary trees encoding the structure of rational numbers both from arithmetic and dynamical point of view. The paper is divided into three parts. The first one is mainly expository and consists in a critical review of rather standard topics such as Stern-Brocot and Farey trees and their connections with continued fraction expansion and the question mark function. In the second part we introduce two classes of (invertible and non-invertible)...

Continued fractions on the Heisenberg group

Anton Lukyanenko, Joseph Vandehey (2015)

Acta Arithmetica

Similarity:

We provide a generalization of continued fractions to the Heisenberg group. We prove an explicit estimate on the rate of convergence of the infinite continued fraction and several surprising analogs of classical formulas about continued fractions.

Transcendence with Rosen continued fractions

Yann Bugeaud, Pascal Hubert, Thomas A. Schmidt (2013)

Journal of the European Mathematical Society

Similarity:

We give the first transcendence results for the Rosen continued fractions. Introduced over half a century ago, these fractions expand real numbers in terms of certain algebraic numbers.