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Abstract numeration systems encode natural numbers using radix ordered words of an infinite regular language and linear recurrence sequences play a key role in their valuation. Sequence automata, which are deterministic finite automata with…
Piecewise smooth systems are intensively studied today in many application areas, such as economics, finance, engineering, biology, and ecology. In this work, we consider a class of one-dimensional piecewise linear discontinuous maps with a…
We formulate general rules for a coarse-graining of the dynamics, which we term `symbolic dynamics', of feedback networks with monotone interactions, such as most biological modules. Networks which are more complex than simple cyclic…
In a recent paper as an alternative to models based on the notion of ideal mathematical point, characterized by a property of separatedness, we considered a viewpoint based on the notion of continuous change, making use of elements of a…
The definition of subshifts of finite symbolic rank is motivated by the finite rank measure-preserving transformations which have been extensively studied in ergodic theory. In this paper we study subshifts of finite symbolic rank as…
To a subshift over a finite alphabet, one can naturally associate an infinite family of finite graphs, called its Rauzy graphs. We show that for a subshift of subexponential complexity the Rauzy graphs converge to the line $\mathbf{Z}$ in…
Building upon [1], this study aims to introduce fractal geometry into graph theory, and to establish a potential theoretical foundation for complex networks. Specifically, we employ the method of substitution to create and explore…
A procedure to obtain the symbolic dynamics for conservative dynamical systems is introduced with reference to the standard map in a strongly chaotic regime. The method extends an approach previously developed for highly dissipative…
Dynamical systems at the edge of chaos, which have been considered as models of self-organization phenomena, are marked by their ability to perform nontrivial computations. To distinguish them from systems with limited computing power, we…
Orbital fuzzy iterated function systems are obtained as a combination of the concepts of iterated fuzzy set system and orbital iterated function system. It turns out that, for such a system, the corresponding fuzzy operator is weakly…
For any dynamical system $T:X\rightarrow X$ of a compact metric space $X$ with $g-$almost product property and uniform separation property, under the assumptions that the periodic points are dense in $X$ and the periodic measures are dense…
This contribution describes a statistical model for decaying quantum systems (e.g. photo-dissociation or -ionization). It takes the interference between direct and indirect decay processes explicitely into account. The resulting expressions…
Necessary and sufficient conditions for the symbolic dynamics of a Lorenz map to be fully embedded in the symbolic dynamics of a piecewise continuous interval map are given. As an application of this result, we describe a new algorithm for…
Let $X$ be a compact metric space and let $f:X\rightarrow X$ be a homeomorphism on $X$. We show that if $f$ is both pointwise recurrent and expansive, then the dynamical system $(X, f)$ is topologically conjugate to a subshift of some…
We propose an algorithm for the detection of recurrence domains of complex dynamical systems from time series. Our approach exploits the characteristic checkerboard texture of recurrence domains exhibited in recurrence plots (RP). In phase…
In this note we complement recent results on the exchange $r$-matrices appearing in the chiral WZNW model by providing a direct, purely finite-dimensional description of the relationship between the monodromy dependent 2-form that enters…
We describe varieties of minimal rational tangents on the wonderful symmetric varieties by marked Dynkin diagrams. An irreducible component of a variety of minimal rational tangents is a rational homogeneous space, and hence, we have a…
This paper formulates a notion of high-dimensional random dynamical systems that couple to another system, like an embedding environment, in such a way that each system engages in controlled exchange with the other system. Using the…
Open dynamical systems are mathematical models of machines that take input, change their internal state, and produce output. For example, one may model anything from neurons to robots in this way. Several open dynamical systems can be…
Let $M$ be a compact Riemannian manifold. The set $\text{F}^{r}(M)$ consisting of sequences $(f_{i})_{i\in\mathbb{Z}}$ of $C^{r}$-diffeomorphisms on $M$ can be endowed with the compact topology or with the strong topology. A notion of…