Transcendency of Local Conjugacies in Complex Dynamics and Transcendency of their Values.
Tree algebra of sofic tree languages
We consider the languages of finite trees called tree-shift languages which are factorial extensible tree languages. These languages are sets of factors of subshifts of infinite trees. We give effective syntactic characterizations of two classes of regular tree-shift languages: the finite type tree languages and the tree languages which are almost of finite type. Each class corresponds to a class of subshifts of trees which is invariant by conjugacy. For this goal, we define a tree algebra which...
Triangular maps with the chain recurrent points periodic.
Two commuting maps without common minimal points
We construct an example of two commuting homeomorphisms S, T of a compact metric space X such that the union of all minimal sets for S is disjoint from the union of all minimal sets for T. In other words, there are no common minimal points. This answers negatively a question posed in [C-L]. We remark that Furstenberg proved the existence of "doubly recurrent" points (see [F]). Not only are these points recurrent under both S and T, but they recur along the same sequence of powers. Our example shows...
Two point correlation functions for a periodic box-ball system.
Type de tresse d'orbites périodiques
Ultimate boundedness of some third order ordinary differential equations
We prove the ultimate boundedness of solutions of some third order nonlinear ordinary differential equations using the Lyapunov method. The results obtained generalize earlier results of Ezeilo, Tejumola, Reissig, Tunç and others. The Lyapunov function used does not involve the use of signum functions as used by others.
Unbounded solutions of a boundary value problem for abstract th-order differential equations on an infinite interval.
Uncountable ω-limit sets with isolated points
We give two examples of tent maps with uncountable (as it happens, post-critical) ω-limit sets, which have isolated points, with interesting structures. Such ω-limit sets must be of the form C ∪ R, where C is a Cantor set and R is a scattered set. Firstly, it is known that there is a restriction on the topological structure of countable ω-limit sets for finite-to-one maps satisfying at least some weak form of expansivity. We show that this restriction does not hold if the ω-limit set is uncountable....
Une caractérisation simple des nombres de Sturm
Un mot sturmien est la discrétisation d’une droite de pente irrationnelle. Un nombre de Sturm est la pente d’un mot sturmien qui est invariant par une substitution non triviale. Ces nombres sont certains irrationnels quadratiques caractérisés par la forme de leur développement en fraction continue. Nous donnons une caractérisation très simple des nombres de Sturm : un nombre irrationnel positif est de Sturm (de première espèce) si et seulement s’il est quadratique et à conjugué négatif.
Uniformly recurrent sequences and minimal Cantor omega-limit sets
We investigate the structure of kneading sequences that belong to unimodal maps for which the omega-limit set of the turning point is a minimal Cantor set. We define a scheme that can be used to generate uniformly recurrent and regularly recurrent infinite sequences over a finite alphabet. It is then shown that if the kneading sequence of a unimodal map can be generated from one of these schemes, then the omega-limit set of the turning point must be a minimal Cantor set.
Unimodal generalized pseudo-Anosov maps.
Unimodular Pisot substitutions and their associated tiles
Let be a unimodular Pisot substitution over a letter alphabet and let be the associated Rauzy fractals. In the present paper we want to investigate the boundaries () of these fractals. To this matter we define a certain graph, the so-called contact graph of . If satisfies a combinatorial condition called the super coincidence condition the contact graph can be used to set up a self-affine graph directed system whose attractors are certain pieces of the boundaries . From this graph...
Universally finitary symbolic extensions
We prove that by considering a finitary (almost continuous) symbolic extension of a topological dynamical system instead of a continuous extension, one cannot achieve any drop of the entropy of the extension.
Useful properties of index pairs for upper semicontinuous multivalued dynamical systems.
Using density matrices in classical dynamical systems
Wandering domains and invariant conformal structures for mappings of the 2-torus.
Weak mixing and eigenvalues for Arnoux-Rauzy sequences
We define by simple conditions two wide subclasses of the so-called Arnoux-Rauzy systems; the elements of the first one share the property of (measure-theoretic) weak mixing, thus we generalize and improve a counter-example to the conjecture that these systems are codings of rotations; those of the second one have eigenvalues, which was known hitherto only for a very small set of examples.
Weak mixing and product recurrence
In this article we study the structure of the set of weakly product recurrent points. Among others, we provide necessary conditions (related to topological weak mixing) which imply that the set of weakly product recurrent points is residual. Additionally, some new results about the class of systems disjoint from every minimal system are obtained.
Weakly fuzzy topological entropy
In 2005, İ. Tok fuzzified the notion of the topological entropy R. A. Adler et al. (1965) using the notion of fuzzy compactness of C. L. Chang (1968). In the present paper, we have proposed a new definition of the fuzzy topological entropy of fuzzy continuous mapping, namely weakly fuzzy topological entropy based on the notion of weak fuzzy compactness due to R. Lowen (1976) along with its several properties. We have shown that the topological entropy R. A. Adler et al. (1965) of continuous mapping...