Initial powers of Sturmian sequences
Inverse limits of tentlike maps on trees
We investigate generalizations of Ingram's Conjecture involving maps on trees. We show that for a class of tentlike maps on the k-star with periodic critical orbit, different maps in the class have distinct inverse limit spaces. We do this by showing that such maps satisfy the conclusion of the Pseudo-isotopy Conjecture, i.e., if h is a homeomorphism of the inverse limit space, then there is an integer N such that h and σ̂^N switch composants in the same way, where σ̂ is the standard shift map of...
Inverse problems of symbolic dynamics
This paper reviews some results regarding symbolic dynamics, correspondence between languages of dynamical systems and combinatorics. Sturmian sequences provide a pattern for investigation of one-dimensional systems, in particular interval exchange transformation. Rauzy graphs language can express many important combinatorial and some dynamical properties. In this case combinatorial properties are considered as being generated by a substitutional system, and dynamical properties are considered...
Irreducible complexity of iterated symmetric bimodal maps.
Jumps of entropy for interval maps
We study the jumps of topological entropy for interval or circle maps. We prove in particular that the topological entropy is continuous at any with . To this end we study the continuity of the entropy of the Buzzi-Hofbauer diagrams associated to interval maps.
-theory for Cuntz-Krieger algebras arising from real quadratic maps.
Languages of finite words occurring infinitely many times in an infinite word
We give necessary and sufficient conditions for a language to be the language of finite words that occur infinitely many times in an infinite word.
Languages of finite words occurring infinitely many times in an infinite word
We give necessary and sufficient conditions for a language to be the language of finite words that occur infinitely many times in an infinite word.
Lifting Covers of Sofic Shifts.
Local return rates in Sturmian subshifts
Local return rates in substitutive subshifts
Logarithmic frequency in morphic sequences
We study the logarithmic frequency of letters and words in morphic sequences and show that this frequency must always exist, answering a question of Allouche and Shallit.
Matrices of positive polynomials.
Matsumoto -groups associated to certain shift spaces.
Minimal Bratteli diagrams and the dimension groups of AF -algebras.
Minimal polynomials of some beta-numbers and Chebyshev polynomials
Minimal sequences and the Kadison-Singer problem.
Minimal systems and distributionally scrambled sets
In this paper we investigate numerous constructions of minimal systems from the point of view of -chaos (but most of our results concern the particular cases of distributional chaos of type and ). We consider standard classes of systems, such as Toeplitz flows, Grillenberger -systems or Blanchard-Kwiatkowski extensions of the Chacón flow, proving that all of them are DC2. An example of DC1 minimal system with positive topological entropy is also introduced. The above mentioned results answer...
Mixing properties of nearly maximal entropy measures for shifts of finite type
We prove that for a certain class of shifts of finite type with positive topological entropy there is always an invariant measure, with entropy arbitrarily close to the topological entropy, that has strong metric mixing properties. With the additional assumption that there are dense periodic orbits, one can ensure that this measure is Bernoulli.
Monotonous stability for neutral fixed points.