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In this paper, we realize C*-algebras of generalized Boolean dynamical systems as partial crossed products. Reciprocally, we give some sufficient conditions for a partial crossed product to be isomorphic to a C*-algebra of a generalized…
A C*-algebra is n-homogeneous (where n is finite) if every its nonzero irreducible representation acts on an n-dimensional Hilbert space. An elementary proof of Fell's characterization of n-homogeneous C*-algebras (by means of their…
Polynomial dynamical systems are widely used to model and study real phenomena. In biochemistry, they are the preferred choice for modelling the concentration of chemical species in reaction networks with mass-action kinetics. These systems…
In this survey, we study the relations between amenability (resp. amenability at infinity) of C*-dynamical systems and equality or nuclearity (resp. exactness) of the corresponding crossed products.
We survey the use of extra-set-theoretic hypotheses, mainly the continuum hypothesis, in the C*-algebra literature. The Calkin algebra emerges as a basic object of interest.
We study an algebraic analog of a C*-algebra associated to a generalized Boolean dynamical system which parallels the relation between graph C*-algebras and Leavitt path algebras. We prove that such algebras are Cuntz-Pimsner algebras and…
We prove some properties of analytic multiplicative and sub-multiplicative cocycles. The results allow to construct natural invariant analytic sets associated to complex dynamical systems.
We characterize the class of RFD $C^*$-algebras as those containing a dense subset of elements that attain their norm under a finite-dimensional representation. We show further that this subset is the whole space precisely when every…
This paper introduces the notions of atoms and atomicity in $C$-algebras and obtains a characterisation of atoms in the $C$-algebra of transformations. Further, this work presents some necessary conditions and sufficient conditions for the…
Relations between points in the phase space are central to the study of topological dynamical systems. Since many of these relations share common properties, it is natural to study them within a unified framework. To this end, we introduce…
An amorphic association scheme has the property that any of its fusion is also an association scheme. In this paper we generalize the property to be amorphic to an arbitrary C-algebra and prove that any amorphic C-algebra is determined up…
In this paper we study the problem of computing a Kolchin characteristic set of a radical differential ideal. The central part of the article is the presentation of algorithms solving this problem in two principal cases: for ordinary…
Classical Bianchi-Lie, Backlund and Darboux transformations are considered. Their generalizations for the dynamical systems are discussed. For the transformation being the generalization of the normal shift the special class of dynamical…
We have introduced a notion of $C^*$-symbolic dynamical system in [K. Matsumoto: Actions of symbolic dynamical systems on $C^*$-algebras, to appear in J. Reine Angew. Math.], that is a finite family of endomorphisms of a $C^*$-algebra with…
Dynamic networks are structured interconnections of dynamical systems (modules) driven by external excitation and disturbance signals. In order to identify their dynamical properties and/or their topology consistently from measured data, we…
We describe a canonical procedure for associating to any (germ of) holomorphic self-map f of C^n fixing the origin such that df_O is invertible and non-diagonalizable an n-dimensional complex manifold M, a holomorphic map p from M to C^n, a…
We give a positive answer to a question of J. Doyle and J. Silverman about fields of definition of dynamical systems on $\mathbb{P}^{n}$. We prove that, for fixed $n$, there exists a constant $C_{n}$ such that every dynamical system…
052<p type="texpara" tag="Body Text" et="abstract" >A completely $n$ -positive linear map from a locally $C^{\ast}$-algebra $A$ to another locally $C^{\ast}$-algebra $B $is an $n\times n$ matrix whose elements are continuous linear maps…
We provide an explicit method to construct dynamical systems which admit an a-priori prescribed attracting set. As application, we provide a method to construct perturbations of conservative dynamical systems, which admit an a-priori…
Data-driven modeling of dynamical systems often faces numerous data-related challenges. A fundamental requirement is the existence of a unique set of parameters for a chosen model structure, an issue commonly referred to as identifiability.…