Substitutive Arnoux-Rauzy sequences have pure discrete spectrum
نویسندگان
چکیده
We prove that the symbolic dynamical system generated by a purely substitutive Arnoux-Rauzy sequence is measurably conjugate to a toral translation. The proof is based on an explicit construction of a fundamental domain with fractal boundary (a Rauzy fractal) for this toral translation. Communicated by Pierre Liardet Dedicated to the memory of Gérard Rauzy
منابع مشابه
Geometry, Dynamics, and Arithmetic of S-adic Shifts
This paper studies geometric and spectral properties of S-adic shifts and their relation to continued fraction algorithms. Pure discrete spectrum for S-adic shifts and tiling properties of associated Rauzy fractals are established under a generalized Pisot assumption together with a geometric coincidence condition. These general results extend the scope of the Pisot substitution conjecture to t...
متن کاملGeometrical Models for Substitutions
We consider a substitutive version of the Arnoux-Yoccoz Interval Exchange Transformation (IET) related to the Tribonacci substitution. We construct the so-called stepped lines associated to the fixed points of the substitution in the Abelianisation (symbolic) space. We analyse various projections of the stepped line recovering the Rauzy Fractal, a Peano Curve related to the work of Arnoux [1], ...
متن کاملA Generalization of Sturmian Sequences; Combinatorial Structure and Transcendence∗
In this paper we study dynamical properties of a class of uniformly recurrent sequences on a k-letter alphabet with complexity p(n) = (k − 1)n + 1. These sequences, originally defined by P. Arnoux and G. Rauzy, are a natural generalization of the (binary) Sturmian sequences of Morse and Hedlund. We give two combinatorial algorithms for constructing characteristic Arnoux-Rauzy sequences. The fir...
متن کاملFrequencies of Factors in Arnoux-rauzy Sequences
V. Berthé showed that the frequencies of factors in a Sturmian word of slope α, as well as the number of factors with a given frequency, can be expressed in terms of the continued fraction expansion of α. In this paper we describe a multi-dimensional continued fraction process associated with a class of sequences of (block) complexity kn+1 originally introduced by P. Arnoux and G. Rauzy. This v...
متن کاملFactor Complexity of S-adic sequences generated by the Arnoux-Rauzy-Poincaré Algorithm
The Arnoux-Rauzy-Poincaré multidimensional continued fraction algorithm is obtained by combining the Arnoux-Rauzy and Poincaré algorithms. It is a generalized Euclidean algorithm. Its three-dimensional linear version consists in subtracting the sum of the two smallest entries to the largest if possible (Arnoux-Rauzy step), and otherwise, in subtracting the smallest entry to the median and the m...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/1108.5574 شماره
صفحات -
تاریخ انتشار 2011