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The problem of determining the mathematical model of the dynamics of multi-dimensional control systems in the presence of noise under the condition that the correlation functions cannot be found. Known statistical dynamics of linear systems…
In the paper, we study behavior of discrete dynamical systems (automata) w.r.t. transitivity; that is, speaking loosely, we consider how diverse may be behavior of the system w.r.t. variety of word transformations performed by the system:…
This paper will discuss the problem of defining the new topological transitivity. To do this several equivalent topological transitive and non-wandering point has been discussed through this paper. This paper also consider the ideal version…
The past decades have seen increasing interest in modelling uncertainty by heterogeneous methods, combining probability and interval analysis, especially for assessing parameter uncertainty in engineering models. A unifying mathematical…
We study the behaviour of discrete dynamical systems generated by a continuous map $f$ of a compact real interval into itself where at randomly chosen times a function different from $f$ - so called impulse function is applied. We show that…
The automaton transformation of infinite words over alphabet $\mathbb F_p=\{0,1,\ldots,p-1\}$, where $p$ is a prime number, coincide with the continuous transformation (with respect to the $p$-adic metric) of a ring $\mathbb Z_p$ of…
We study the problem of detecting the structure of a complex dynamical system described by a set of deterministic differential equation that contains a Hamiltonian subsystem, without any information on the explicit form of evolution laws.…
It is offered to consider word meanings changes in diachrony as semicontinuous random walk with reflecting and swallowing screens. The basic characteristics of word life cycle are defined. Verification of the model has been realized on the…
In this paper we extend the notion of a continuous bundle random dynamical system to the setting where the action of $\R$ or $\N$ is replaced by the action of an infinite countable discrete amenable group. Given such a system, and a…
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…
Chaotic attractors, chaotic saddles and periodic orbits are examples of chain-recurrent sets. Using arbitrary small controls, a trajectory starting from any point in a chain-recurrent set can be steered to any other in that set. The…
We prove existence of asymptotic entropy of random walks on regular languages over a finite alphabet and we give formulas for it. Furthermore, we show that the entropy varies real-analytically in terms of probability measures of constant…
A sequence of large invertible matrices given by a small random perturbation around a fixed diagonal and positive matrix induces a random dynamics on a high-dimensional sphere. For a certain class of rotationally invariant random…
Deterministic many-body systems governed by simple interactions can self-organize into macroscopic patterns, and the determinants of long-time behavior are assumed to be encoded in the initial configuration. Here we show that predictability…
We begin development of a method for studying dynamical systems using concepts from computational complexity theory. We associate families of decision problems, called telic problems, to dynamical systems of a certain class. These decision…
Singularities in macroscopic systems at discontinuous phase transitions are replaced in finite systems by sharp but continuous changes. Both the energy differences between metastable and stable phases and the energy barriers separating…
For a class of linear switched systems in continuous time a controllability condition implies that state feedbacks allow to achieve almost sure stabilization with arbitrary exponential decay rates. This is based on the Multiplicative…
After a brief historical survey, the paper introduces the notion of entropic model sets (cut and project sets), and, more generally, the notion of diffractive point sets with entropy. Such sets may be thought of as generalizations of…
We define a notion of randomness for individual and collections of formal languages based on automatic martingales acting on sequences of words from some underlying domain. An automatic martingale bets if the incoming word belongs to the…
In this work we explore the ability of the Google search engine to find results for random N-letter strings. These random strings, dense over the set of possible N-letter words, address the existence of typos, acronyms, and other words…