Manfred Denker, Atsushi Imai, Susanne Koch (2007)
Colloquium Mathematicae
We define thin equivalence relations ∼ on shift spaces and derive Dirichlet forms on the quotient space in terms of the nearest neighbour averaging operator. We identify the associated Laplace operator. The conditions are applied to some non-self-similar extensions of the Sierpiński gasket.
Valérie Berthé (2009)
Actes des rencontres du CIRM
Guy Barat, Valérie Berthé, Pierre Liardet, Jörg Thuswaldner (2006)
Annales de l’institut Fourier
This survey aims at giving a consistent presentation of numeration from a dynamical viewpoint: we focus on numeration systems, their associated compactification, and dynamical systems that can be naturally defined on them. The exposition is unified by the fibred numeration system concept. Many examples are discussed. Various numerations on rational integers, real or complex numbers are presented with special attention paid to -numeration and its generalisations, abstract numeration systems and...
Gabriel Vigny (2007)
Publicacions Matemàtiques
We study the dynamics near infinity of polynomial mappings f in C2. We assume that f has indeterminacy points and is non constant on the line at infinity L∞. If L∞ is f-attracting, we decompose the Green current along itineraries defined by the indeterminacy points and their preimages. The symbolic dynamics that arises is a subshift on an infinite alphabet.
Guy Barat, Tomasz Downarowicz, Pierre Liardet (2002)
Acta Arithmetica
Sébastien Ferenczi, Luca Q. Zamboni (2011)
Annales scientifiques de l'École Normale Supérieure
For a class of -interval exchange transformations, which we call the symmetric class, we define a new self-dual induction process in which the system is successively induced on a union of sub-intervals. This algorithm gives rise to an underlying graph structure which reflects the dynamical behavior of the system, through the Rokhlin towers of the induced maps. We apply it to build a wide assortment of explicit examples on four intervals having different dynamical properties: these include the first...
Ethan M. Coven, Reem Yassawi (2009)
Fundamenta Mathematicae
We consider the problem of embedding odometers in one-dimensional cellular automata. We show that (1) every odometer can be embedded in a gliders-with-reflecting-walls cellular automaton, which one depending on the odometer, and (2) an odometer can be embedded in a cellular automaton with local rule (i ∈ ℤ), where n depends on the odometer, if and only if it is “finitary.”
Charles Holton, Brian F. Martensen (2008)
Fundamenta Mathematicae
We show that an aperiodic minimal tiling space with only finitely many asymptotic composants embeds in a surface if and only if it is the suspension of a symbolic interval exchange transformation (possibly with reversals). We give two necessary conditions for an aperiodic primitive substitution tiling space to embed in a surface. In the case of substitutions on two symbols our classification is nearly complete. The results characterize the codimension one hyperbolic attractors of surface diffeomorphisms...
Jacques Justin (2005)
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
We associate with a word on a finite alphabet an episturmian (or Arnoux-Rauzy) morphism and a palindrome. We study their relations with the similar ones for the reversal of . Then when we deduce, using the sturmian words that are the fixed points of the two morphisms, a proof of a Galois theorem on purely periodic continued fractions whose periods are the reversal of each other.
Jacques Justin (2010)
RAIRO - Theoretical Informatics and Applications
We associate with a word w on a finite alphabet A an episturmian (or Arnoux-Rauzy) morphism and a palindrome. We study their relations with the similar ones for the reversal of w. Then when |A|=2 we deduce, using the Sturmian words that are the fixed points of the two morphisms, a proof of a Galois theorem on purely periodic continued fractions whose periods are the reversal of each other.
Matsumoto, Kengo (2011)
Documenta Mathematica
Rafael Labarca, Carlos Gustavo Moreira (2006)
Annales de l'I.H.P. Analyse non linéaire
Yang, Xiao-Song, Bai, Xiaoming (2006)
Discrete Dynamics in Nature and Society
Kennison, John F. (2009)
Theory and Applications of Categories [electronic only]
Henk Bruin, Alexandra Kaffl, Dierk Schleicher (2009)
Fundamenta Mathematicae
A (quadratic) Hubbard tree is an invariant tree connecting the critical orbit within the Julia set of a postcritically finite (quadratic) polynomial. It is easy to read off the kneading sequences from a quadratic Hubbard tree; the result in this paper handles the converse direction. Not every sequence on two symbols is realized as the kneading sequence of a real or complex quadratic polynomial. Milnor and Thurston classified all real-admissible sequences, and we give a classification of all complex-admissible...
Frédéric Naud (2005)
Annales scientifiques de l'École Normale Supérieure
Tomasz Downarowicz, Dawid Huczek (2012)
Studia Mathematica
We prove that every topological dynamical system (X,T) has a faithful zero-dimensional principal extension, i.e. a zero-dimensional extension (Y,S) such that for every S-invariant measure ν on Y the conditional entropy h(ν | X) is zero, and, in addition, every invariant measure on X has exactly one preimage on Y. This is a strengthening of the authors' result in Acta Appl. Math. [to appear] (where the extension was principal, but not necessarily faithful).
Papini, Duccio, Zanolin, Fabio (2004)
Fixed Point Theory and Applications [electronic only]
Julien Cassaigne, Nataliya Chekhova (2006)
Annales de l’institut Fourier
La fonction de récurrence d’une suite symbolique compte au bout de combien de temps on voit tous les mots de longueur . Nous la calculons explicitement pour les suites d’Arnoux-Rauzy, définies par des conditions combinatoires qui en font une généralisation naturelle des suites sturmiennes. Puis nous répondons à une question de Morse et Hedlund (1940) en montrant que ne peut avoir une limite finie pour aucune suite non ultimement périodique.
Collins, Pieter (2005)
Experimental Mathematics