Internationally recognised researchers look at develo** trends in combinatorics with
applications in the study of words and in symbolic dynamics. They explain the important …

We construct a natural extension for each of Nakada's α-continued fraction transformations
and show the continuity as a function of α of both the entropy and the measure of the natural …

Recently, Edward Burger and his co-authors introduced and studied in Burger et al.(2008)[3]
a new class of continued fraction algorithms. In particular they showed that for every …

We introduce a random dynamical system related to continued fraction expansions. It uses
random combinations of the Gauss map and the Rényi (or backwards) continued fraction …

Invariant Measures, Matching and the Frequency of 0 for Signed Binary Expansions Page 1
Publ. RIMS Kyoto Univ. 56 (2020), 701–742 DOI 10.4171/PRIMS/56-4-2 Invariant Measures …

We investigate matching for the family T α (x)= β x+ α (mod 1), α∈[0, 1], for fixed β> 1.
Matching refers to the property that there is an n∈ N such that T α n (0)= T α n (1). We show …

We adjust Arnoux's coding, in terms of regular continued fractions, of the geodesic flow on
the modular surface to give a cross section on which the return map is a double cover of the …

In this paper we discuss a coding and the associated symbolic dynamics for the geodesic
flow on Hecke triangle surfaces. We construct an explicit cross section for which the first …

As a natural counterpart to Nakada's $\alpha $-continued fraction maps, we study a one-
parameter family of continued fraction transformations with an indifferent fixed point. We …

We prove the convergence and ergodicity of a wide class of real and higher-dimensional
continued fraction algorithms, including folded and-type variants of complex, quaternionic …