Related papers: Synchronizing Dynamical Systems: Finitely presente…

Building on work of Ruelle and Putnam in the Smale space case, Thomsen defined the homoclinic and heteroclinic $C^\ast$-algebras for an expansive dynamical system. In this paper we define a class of expansive dynamical systems, called…

Building on our previous work, we give a thorough presentation of the techniques developed for synchronizing dynamical systems in the special case of synchronizing shift spaces. Following work of Thomsen, we give a construction of the…

In the first part of the paper, we introduce notions of asymptotic continuous orbit equivalence and asymptotic conjugacy in Smale spaces and characterize them in terms of their asymptotic Ruelle algebras with their dual actions. In the…

We continue the study of the Fourier-Stieltjes algebra of a C$^\ast$-dynamical system, initiated by B\'edos and Conti, and recently extended by Buss, Kwa\'sniewski, McKee and Skalski. Firstly, we introduce and study a natural notion of a…

We consider C*-algebras associated with stable and unstable equivalence in hyperbolic dynamical systems known as Smale spaces. These systems include shifts of finite type, in which case these C*-algebras are both AF-algebras. These algebras…

We define and study a class of finite topological spaces, which model the cell structure of a space obtained by gluing finitely many Euclidean convex polyhedral cells along congruent faces. We call these finite topological spaces,…

We study a C*-dynamical system arising from the ring inclusion of the 2\times 2 integer matrices in the rational ones. The orientation preserving affine groups of these rings form a Hecke pair that is closely related to a recent…

Finite topological spaces are in bijective correspondence with preorders on finite sets. We undertake their study using combinatorial tools that have been developed to investigate general discrete structures. A particular emphasis will be…

A tiling with infinite rotational symmetry, such as the Conway-Radin Pinwheel Tiling, gives rise to a topological dynamical system to which an \'etale equivalence relation is associated. A groupoid C*-algebra for a tiling is produced and a…

This paper reveals a categorical equivalence connecting two distinct quantum logic structures. The first is the orthomodular lattice, an algebraic system designed to formalize the properties of quantum systems. The second is a finitary…

Systems obtained by quotienting a subshift of finite type (SFT) by another SFT are called finitely presented in the literature. Analogously, if a sofic shift is quotiented by a sofic equivalence relation, we call the resulting system…

The main result of this paper is the evidence of an explicit linearization of dynamical systems of Ruijsenaars-Schneider type and of the perturbations introduced by F. Calogero of these systems with all orbits periodic of same period.…

We introduce "synchronous algebras", an algebraic structure tailored to recognize automatic relations (aka. synchronous relations, or regular relations). They are the equivalent of monoids for regular languages, however they conceptually…

This paper is meant to be a short review and summary of recent results on the structure of finite and affine classical W-algebras, and the application of the latter to the theory of generalized Drinfeld-Sokolov hierarchies.

Buchholz and Grundling (Comm. Math. Phys., 272, 699--750, 2007) introduced a C$^\ast$-algebra called the resolvent algebra as a canonical quantisation of a symplectic vector space, and demonstrated that this algebra has several desirable…

We present a graph-theoretic model for dynamical systems $(X,\sigma)$ given by a surjective local homeomorphism $\sigma$ on a totally disconnected compact metrizable space $X$. In order to make the dynamics appear explicitly in the graph,…

Classical Ramsey theory has successfully extended to relational structures, yielding a wealth of results that have profoundly influenced other areas of mathematics. Interestingly, the same development has not occurred in the case of dual…

The K-theoretic analog of Spanier-Whitehead duality for noncommutative C*-algebras is shown to hold for the Ruelle algebras associated to irreducible Smale spaces. This had previously been proved only for shifts of finite type. Implications…

We associate to each discrete partial dynamical system a universal C*-algebra generated by partial isometries satisfying relations given by a Boolean algebra connected to the discrete partial dynamical system in question. We show that for…

We review some recent advances in modular representation theory of symmetric groups and related Hecke algebras. We discuss connections with Khovanov-Lauda-Rouquier algebras and gradings on the blocks of the group algebras $F\Sigma_n$, which…