Related papers: Random product of substitutions with the same inci…
Separated graphs provide a powerful combinatorial tool for approximating dynamical systems. This paper details the explicit construction of Bratteli-like separated graphs -- a generalization of classical Bratteli diagrams -- that encode the…
We present a method based on symbolic dynamics for the detection of synchronization in networks of coupled maps and distinguishing between chaotic and random iterations. The symbolic dynamics are defined using special partitions of the…
We use symbolic dynamics to study discrete-time dynamical systems with multiple time delays. We exploit the concept of avoiding sets, which arise from specific non-generating partitions of the phase space and restrict the occurrence of…
We consider the dynamical behavior of Martin-L\"of random points in dynamical systems over metric spaces with a computable dynamics and a computable invariant measure. We use computable partitions to define a sort of effective symbolic…
Primitive constant length substitutions generate minimal symbolic dynamical systems. In this article we present an algorithm which can produce the list of injective substitutions of the same length that generate topologically conjugate…
Spatio-temporal network dynamics is an emergent property of many complex systems which remains poorly understood. We suggest a new approach to its study based on the analysis of dynamical motifs -- small subnetworks with periodic and…
Diagonalizability plays an important role in the analysis and design of multivariable systems. A structured matrix is called structurally diagonalizable if almost all of its numerical realizations, obtained by assigning real values to its…
In this paper we examine the interplay between recurrence properties and the shadowing property in dynamical systems on compact metric spaces. In particular, we demonstrate that if the dynamical system $(X,f)$ has shadowing, then it is…
We introduce a new analytical method, which allows to find out chaotic dynamics in non-smooth dynamical systems. A simple mechanical system consisting of a mass and a dry friction element is considered as an example. The corresponding…
For a product of i.i.d. random maps or a memoryless stochastic flow on a compact space $X$, we find conditions under which the presence of locally asymptotically stable trajectories (e.g. as given by negative Lyapunov exponents) implies…
Symbolic regression is a powerful system identification technique in industrial scenarios where no prior knowledge on model structure is available. Such scenarios often require specific model properties such as interpretability, robustness,…
The dynamics of a linear dynamical system over a finite field can be described by using the elementary divisors of the corresponding matrix. It is natural to extend the investigation to a general finite commutative ring. In a previous…
The Rauzy fractal is a domain in the two-dimensional plane constructed by the Rauzy substitution, a substitution rule on three letters. The Rauzy fractal has a fractal-like boundary, and the currently known its constructions is not only for…
The concept of random dynamical system is a comparatively recent development combining ideas and methods from the well developed areas of probability theory and dynamical systems. Due to our inaccurate knowledge of the particular physical…
We consider the category of partially observable dynamical systems, to which the entropy theory of dynamical systems extends functorially. This leads us to introduce quotient-topological entropy. We discuss the structure that emerges. We…
We study how a coupled array of spiking chaotic systems synchronizes to an external driving in a short time. Synchronization means spike separation at adjacent sites much shorter than the average inter-spike interval; a local lack of…
We develop some aspects of a general theory of presentations of subshifts by labelled directed graphs, in particular by compact graphs. Also considered are synchronization properties of subshifts that lead to presentations by countable…
Self-inducing structure of pentagonal piecewise isometry is applied to show detailed description of periodic and aperiodic orbits, and further dynamical properties. A Pisot number appears as a scaling constant and plays a crucial role in…
We consider a discrete dynamical system on a compact manifold M generated by a homeomorphism f. Let C = {M(i)} be a finite covering of M by closed cells. The symbolic image of a dynamical system is a directed graph G with vertices…
This paper is a survey, with few proofs, of ideas and notions related to self-similarity of groups, semi-groups and their actions. It attempts to relate these concepts to more familiar ones, such as fractals, self-similar sets, and…