Displaying similar documents to “Local return rates in substitutive subshifts”

A graph approach to computing nondeterminacy in substitutional dynamical systems

Toke M. Carlsen, Søren Eilers (2007)

RAIRO - Theoretical Informatics and Applications

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We present an algorithm which for any aperiodic and primitive substitution outputs a finite representation of each special word in the shift space associated to that substitution, and determines when such representations are equivalent under orbit and shift tail equivalence. The algorithm has been implemented and applied in the study of certain new invariants for flow equivalence of substitutional dynamical systems.

Système dynamique à spectre discret et pavage périodique associé à une substitution

Anne Siegel (2004)

Annales de l'Institut Fourier

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On donne une condition combinatoire effective suffisante pour que le sytème dynamique associé à une substitution de type Pisot ait un spectre purement discret. Dans le cas unimodulaire, cette condition est nécessaire dès que la substitution n'a qu'un cobord trivial ; elle est vérifiée si et seulement si le fractal de Rauzy associé à la substitution engendre un pavage auto-similaire et périodique. On en déduit des conditions de connexité des fractals de Rauzy....

Hereditary properties of words

József Balogh, Béla Bollobás (2005)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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Let 𝒫 be a hereditary property of words, i.e., an infinite class of finite words such that every subword (block) of a word belonging to 𝒫 is also in 𝒫 . Extending the classical Morse-Hedlund theorem, we show that either 𝒫 contains at least n + 1 words of length n for every n or, for some N , it contains at most N words of length n for every n . More importantly, we prove the following quantitative extension of this result: if 𝒫 has m ≤ n words of length n then, for every k ≥ n + m , it contains at most...

On Christoffel classes

Jean-Pierre Borel, Christophe Reutenauer (2006)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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We characterize conjugation classes of Christoffel words (equivalently of standard words) by the number of factors. We give several geometric proofs of classical results on these words and sturmian words.