In this chapter, we will study symbolic sequences generated by an irrational rotation. Such
sequences appear each time a dynamical system has two rationally independent periods; …

Mathematical billiards describe the motion of a mass point in a domain with elastic
reflections off the boundary or, equivalently, the behavior of rays of light in a domain with …

Publisher Summary The theory of mathematical billiards can be partitioned into three areas:
convex billiards with smooth boundaries, billiards in polygons (and polyhedra), and …

Complexity of sequences and dynamical systems Page 1 Discrete Mathematics 206 (1999)
145–154 www.elsevier.com/locate/disc Complexity of sequences and dynamical systems …

Infinite episturmian words are a generalization of Sturmian words which includes the Arnoux–
Rauzy sequences. We continue their study and that of episturmian morphisms, begun …

In this paper, we survey the rich theory of infinite episturmian words which generalize to any
finite alphabet, in a rather resembling way, the well-known family of Sturmian words on two …

The objective pursued in this paper is two-fold. The first part addresses the following
combinatorial problem: is it possible to construct an infinite sequence over n letters where …

We study a two-dimensional generalization of Sturmian sequences corresponding to an
approximation of a plane: these sequences are defined on a three-letter alphabet and code …

This work has been made possible largely thanks to the kind support of the Van Gogh
project N. 98001" Multimodularity and Control"(French-Dutch scientific cooperation project) …

This article presents a survey about balanced words. The balance property comes from
combinatorics on words and is used as a characteristic property of the well-known Sturmian …