Related papers: Function Dynamics
We obtain asymptotic and exact formulae of growth functions for some families of $n$-valued coset groups. We also describe connections between the theory of $n$-valued groups and Symbolic Dynamics.
Physical systems with symmetries are described by functions containing kinematical and dynamical parts. We consider the case when kinematical symmetries are described by a noncompact semisimple real Lie group $G$. Then separation of…
In this paper we describe the dynamics of certain rational maps of the form $k \cdot (x+x^{-1})$ over finite fields of odd characteristic.
This paper is motivated by the theory of sequential dynamical systems, developed as a basis for a mathematical theory of computer simulation. It contains a classification of finite dynamical systems on binary strings, which are obtained by…
In the one-parameter family of power-law maps of the form $f_a(x)=-|x|^{\alpha}+a,$ $\alpha >1,$ we give examples of mutually related dynamically determined quantities, depending on the parameter $a$, such that one is a Pick function of the…
Intermittent maps of the interval are simple and widely-studied models for chaos with slow mixing rates, but have been notoriously resistant to numerical study. In this paper we present an effective framework to compute many ergodic…
Homoclinic and heteroclinic motions in dynamics equations on time scales is investigated. The utilized time scale is a specific one such that it is a union of disjoint compact intervals. A numerical example that supports the theoretical…
The simple realistic model of the tippe top is considered. An averaged system of equations of motion is obtained in special evolutionary variables. Through the qualitative analysis of this system the general features of the motion of the…
We consider the system of $N$ points on the segment of the real line with the nearest-neighbor Coulomb repulsive interaction and external force $F$. For the fixed points of such systems (fixed configurations) we study the asymptotics (in…
Geometric properties of the fixed point set $Fix(f)$ of a self-mapping $f$ on a metric or a generalized metric space is an attractive issue. The set $Fix(f)$ can contain a geometric figure (a circle, an ellipse, etc.) or it can be a…
Functional depth is used for ranking functional observations from most outlying to most typical. The ranks produced by functional depth have been proposed as the basis for functional classifiers, rank tests, and data visualization…
A parking function of length $n$ is a sequence $\pi=(\pi_1,\dots, \pi_n)$ of positive integers such that if $\lambda_1\leq\cdots\leq \lambda_n$ is the increasing rearrangement of $\pi_1,\dots,\pi_n$, then $\lambda_i\leq i$ for $1\leq i\leq…
The relationship of network structure and dynamics is one of most extensively investigated problems in the theory of complex systems of the last years. Understanding this relationship is of relevance to a range of disciplines -- from…
We prove that return time statistics of a dynamical system do not change if one passes to an induced (i.e. first return) map. We apply this to show exponential return time statistics in i) smooth interval maps with nowhere-dense critical…
We introduce the novel concept of a non-stationary iterated function system by considering a countable sequence of distinct set-valued maps $\{\mathcal{F}_k\}_{k\in \mathbb{N}}$ where each $\mathcal{F}_k$ maps $\mathcal{H}(X)\to…
In this paper we propose an elementary topological approach which unifies and extends various different results concerning fixed points and periodic points for maps defined on sets homeomorphic to rectangles embedded in euclidean spaces. We…
Functional networks provide a topological description of activity patterns in the brain, as they stem from the propagation of neural activity on the underlying anatomical or structural network of synaptic connections. This latter is well…
Canonical functions are a powerful concept with numerous applications in the study of groups, monoids, and clones on countable structures with Ramsey-type properties. In this short note, we present a proof of the existence of canonical…
The scope of the paper is the theoretical analysis of the time rate in which a dynamical system reaches a stable stationary state or stable oscillations. The method used for the analysis is based on the so-called iterative time profiles,…
We construct a H\"older continuous function on the unit interval which coincides in uncountably (in fact continuum) many points with every function of total variation smaller than 1 passing through the origin. We say that a function with…