Related papers: Chaotic tracial dynamics

The usual crossed product construction which associates to the homeomorphism $T$ of the locally compact space $X$ the C$^*$-algebra $C^*(X,T)$ is extended to the case of a partial local homeomorphism $T$. For example, the Cuntz-Krieger…

We define and systematically study nonassociative C*-algebras as C*-algebras internal to a topological tensor category. We also offer a concrete approach to these C*-algebras, as G-invariant, norm closed *-subalgebras of bounded operators…

Let A be a unital separable C*-algebra, and D a K_1-injective strongly self-absorbing C*-algebra. We show that if A is D-absorbing, then the crossed product of A by a compact second countable group or by Z or by R is D-absorbing as well,…

We study the Rokhlin dimension for actions of residually finite groups on C*-algebras. We give a definition equivalent to the original one due to Szabo, Wu and Zacharias. We then prove a number of permanence properties and discuss actions…

In this paper, we introduce the notion of a dual topological graph of a given topological graph, and show that it defines a C*-algebra isomorphic to the C*-algebra of the given one. Repeating to take a dual, and taking a projective limit,…

For a number of properties of C*-algebras, including real rank zero, stable rank one, pure infiniteness, residual hereditary infiniteness, the combination of pure infiniteness and the ideal property, the property of being an AT algebra with…

Using Kirchberg-Phillips' classification of purely infinite C*-algebras by K-theory, we prove that the isomorphism types of crossed product C*-algebras associated to certain hyperbolic 3-manifold groups acting on their Gromov boundary only…

In this paper we study chaotic behavior of actions of a countable discrete group acting on a compact metric space by self-homeomorphisms. For actions of a countable discrete group G, we introduce local weak mixing and Li-Yorke chaos; and…

We compute the K-theory for C*-algebras naturally associated with rings of integers in number fields. The main ingredient is a duality theorem for arbitrary global fields. It allows us to identify the crossed product arising from affine…

We examine the ideal structure of crossed products B\rtimes G where B is a continuous-trace C*-algebra and the induced action of G on the spectrum of B is proper. In particular, we are able to obtain a concrete description of the topology…

Chaotic dynamics can be quite heterogeneous in the sense that in some regions the dynamics are unstable in more directions than in other regions. When trajectories wander between these regions, the dynamics is complicated. We say a chaotic…

We define and examine sequentially split $*$-homomorphisms between $\mathrm{C}^*$-algebras and $\mathrm{C}^*$-dynamical systems. For a $*$-homomorphism, the property of being sequentially split can be regarded as an approximate weakening of…

In this paper, a new invariant was built towards the classification of separable C*-algebras of real rank zero, which we call latticed total K-theory. A classification theorem is given in terms of such an invariant for a large class of…

In this paper we define a Rokhlin property for automorphisms of non-unital C*-algebras and for endomorphisms. We show that the crossed product of a C*-algebra by a Rokhlin automorphism preserves absorption of a strongly self-absorbing…

We give a description of traces on C(X)\rtimes G in terms of measurable fields of traces on the C*-algebras of the stabilizers of the action of G on X.

Let X be an infinite compact metric space, \alpha : X \to X a minimal homeomorphism, u the unitary implementing \alpha in the transformation group C*-algebra, and S a class of separable nuclear C*-algebras that contains all unital…

Fundamental problems of periodicity and transient process to periodicity of chaotic trajectories in computer realization with finite computation precision is investigated by taking single and coupled Logistic maps as examples. Empirical…

Pairs of numerically computed trajectories of a chaotic system may coalesce because of finite arithmetic precision. We analyse an example of this phenomenon, showing that it occurs surprisingly frequently. We argue that our model belongs to…

A discrete group is said to be C*-simple if its reduced C*-algebra is simple, and is said to have the unique trace property if its reduced C*-algebra has a unique tracial state. A dynamical characterization of C*-simplicity was recently…

We characterise simplicity of twisted C*-algebras of row-finite k-graphs with no sources. We show that each 2-cocycle on a cofinal k-graph determines a canonical second-cohomology class for the periodicity group of the graph. The groupoid…