Related papers: Amorphic complexity and entropy for symbolic model…
We consider symbolic flows over finite alphabets and study certain kinds of repetitions in these sequences. Positive and negative results for the existence of such repetitions are given for codings of interval exchange transformations and…
Given a compact topological dynamical system (X, f) with positive entropy and upper semi-continuous entropy map, and any closed invariant subset $Y \subset X$ with positive entropy, we show that there exists a continuous roof function such…
The objective of this paper is the proof of a conjecture of Kontsevich on the isomorphism between groups of polynomial symplectomorphisms and automorphisms of the corresponding Weyl algebra in characteristic zero. The proof is based on the…
We prove that the entropy map for countable Markov shifts of finite entropy is upper semi-continuous at ergodic measures. Note that the phase space is non-compact. Applications to systems that can be coded by these shifts, such as positive…
Domino tilings have been studied extensively for both their statistical properties and their dynamical properties. We construct a subshift of finite type using matching rules for several types of dominos. We combine the previous results…
The Hermitian, complex and fermionic two-matrix models with infinite set of variables are constructed. We show that these two-matrix models can be realized by the $W$-representations. In terms of the $W$-representations, we derive the…
A central issue of the science of complex systems is the quantitative characterization of complexity. In the present work we address this issue by resorting to information geometry. Actually we propose a constructive way to associate to a -…
The dynamics of symbolic systems, such as multidimensional subshifts of finite type or cellular automata, are known to be closely related to computability theory. In particular, the appropriate tools to describe and classify topological…
We propose a new way to measure the balance between freedom and coherence in a dynamical system and a new measure of its internal variability. Based on the concept of entropy and ideas from neuroscience and information theory, we define…
In this paper we derived a variational principle for the specific entropy on the context of symbolic dynamics of compact metric space alphabets and use this result to obtain the uniqueness of the equilibrium states associated to a Walters…
A sofic approximation to a countable group is a sequence of partial actions on finite sets that asymptotically approximates the action of the group on itself by left-translations. A group is sofic if it admits a sofic approximation. Sofic…
We study substructures of the Weyl group of conformal transformations of the metric of (pseudo)Riemannian manifolds. These substructures are identified by differential constraints on the conformal factors of the transformations which are…
Topological entropy or spatial entropy is a way to measure the complexity of shift spaces. This study investigates the relationships between the spatial entropy and the various periodic entropies which are computed by skew-coordinated…
We show that the quasi-continuous gapless spectrum of Andreev bound states in multi-terminal semi-classical superconducting nanostructures exhibits a big number of topological singularities. We concentrate on Weyl points in a 4-terminal…
We characterize disjoint and simultaneously hypercyclic tuples of unilateral pseudo-shift operators on $\ell^p(\mathbb{N})$. As a consequence, complementing the results of Bernal and Jung, we give a characterization for simultaneously…
We study suspension flows defined over sub-shifts of finite type with continuous roof functions. We prove the existence of suspension flows with uncountably many ergodic measures of maximal entropy. More generally, we prove that any…
Quantization of a toy model of a pseudointegrable Hamiltonian impact system is introduced, including EBK quantization conditions, a verification of Weyl's law, the study of their wavefunctions and a study of their energy levels properties.…
This is the first part in a series in which sofic entropy theory is generalized to class-bijective extensions of sofic groupoids. Here we define topological and measure entropy and prove invariance. We also establish the variational…
We consider families of coded systems that contain the Dyck shifts and that are closed under topological conjugacy. We introduce a notion of hyposynchronization of subshifts. We introduce a notion of restricted complexity of…
In this article we study automorphisms of Toeplitz subshifts. Such groups are abelian and any finitely generated torsion subgroup is finite and cyclic. When the complexity is non superlinear, we prove that the automorphism group is, modulo…