Related papers: Linear Dynamical Systems
The dynamics by iteration of a function on a compact metric space, sometimes called a cascade, can be extended to the dynamics of a closed relation on such a space. Here we apply this relation dynamics to study semiflows (and their relation…
Physical systems with symmetry arise abundantly in applications, and are endowed with interesting mathematical structures. The present paper focusses on linear reciprocal and input-output Hamiltonian systems. Their characterization is…
Since its establishment, propositional dynamic logic (PDL) has been a subject of intensive academic research and frequent use in the industry. We have studied the complexity of some PDL problems and in this paper, we show results for some…
The paper is a survey of notions and results related to classical and new generalizations of the notion of a periodic sequence. The topics related to almost periodicity in combinatorics on words, symbolic dynamics, expressibility in logical…
We give a summary on the recent development of chaos theory in topological dynamics, focusing on Li-Yorke chaos, Devaney chaos, distributional chaos, positive topological entropy, weakly mixing sets and so on, and their relationships.
I give a short review of the theory of twisted symmetries of differential equations, emphasizing geometrical aspects. Some open problems are also mentioned.
We give a survey on classical and recent applications of dynamical systems to number theoretic problems. In particular, we focus on normal numbers, also including computational aspects. The main result is a sufficient condition for…
The multitime multiple recurrences are common in analysis of algorithms, computational biology, information theory, queueing theory, filters theory, statistical physics etc. The theoretical part about them is little or not known. That is…
We study hyperbolic systems of one-dimensional partial differential equations under general, possibly non-local boundary conditions. A large class of evolution equations, either on individual 1-dimensional intervals or on general networks,…
This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…
We propose a high dimensional generalisation of the standard Klein bottle, going beyond those considered previously. We address the problem of generating continuous scalar fields (distributions) and dynamical systems (flows) on such state…
Linear finite dynamical systems play an important role, for example, in coding theory and simulations. Methods for analyzing such systems are often restricted to cases in which the system is defined over a field %and usually strive to…
These expository notes present a proof of the Stable/Unstable Manifold Theorem (also known as the Hadamard--Perron Theorem). They also give examples of hyperbolic dynamics: geodesic flows on surfaces of negative curvature and dispersing…
In this paper, we study the linear dynamical properties of shift operators on some classes of Segal algebras. Moreover, we characterize hypercyclic generalized bilateral shift operators on the standard Hilbert module.
In this article we develop a general technique which takes a known characterization of a property for weighted backward shifts and lifts it up to a characterization of that property for a large class of operators on $L^p(X)$. We call these…
An thorough introduction is given at an introductory level to the field of quantitative complex system science, with special emphasis on emergence in dynamical systems based on network topologies. Subjects treated include graph theory and…
We introduce a new broad and exible class of multivariate elliptically symmetric distributions in- cluding the elliptically symmetric logistic and multivariate normal. Various probabilistic properties of the new distribution are studied,…
The present article presents a summarizing view at differential-algebraic equations (DAEs) and analyzes how new application fields and corresponding mathematical models lead to innovations both in theory and in numerical analysis for this…
This short note is devoted to the representative dynamics, which realizes a link between the theory of controlled systems and representation theory. Dynamical inverse problem of representation theory for controlled systems is considered: to…
Expansivity, Li-Yorke chaos and shadowing are popular and well-studied notions of dynamical systems. Several simple and useful characterizations of these notions within the setting of linear dynamics were obtained recently. We explore these…