Related papers: Unique ergodicity of circle and interval exchange …
This paper presents a general and systematic discussion of various symbolic representations of iterated maps through subshifts. We give a unified model for all continuous maps on a metric space, by representing a map through a general…
Let $S$ be a planar point set in general position, and let $\mathcal{P}(S)$ be the set of all plane straight-line paths with vertex set $S$. A flip on a path $P \in \mathcal{P}(S)$ is the operation of replacing an edge $e$ of $P$ with…
Recalling the construction of a flat surface from a Bratteli diagram, this paper considers the dynamics of the shift map on the space of all bi-infinite Bratteli diagrams as the renormalizing dynamics on a moduli space of flat surfaces of…
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…
This paper uses the theory of covering graphs to characterize some of the edge-transitive graphs which can arise as token graphs.
In this work, we present several new findings regarding the concepts of orbit-transitivity, strict orbit-transitivity, $\omega$-transitivity, and $\mu$-open-set transitivity for self-maps on generalized topological spaces. Let $(X,\mu)$…
We consider the electromagnetic field in a cavity with a periodically oscillating perfectly reflecting boundary and show that the mathematical theory of circle maps leads to several physical predictions. Notably, well-known results in the…
In this paper, we examine various types of ${\mathcal F}$-hypercyclic (${\mathcal F}$-topologically transitive) and disjoint ${\mathcal F}$-hypercyclic (disjoint ${\mathcal F}$-topologically transitive) properties of binary relations over…
The exchange graph of a cluster algebra encodes the combinatorics of mutations of clusters. Through the recent "categorifications" of cluster algebras using representation theory one obtains a whole variety of exchange graphs associated…
We investigate iterated function systems (IFS) that randomly alternate between two non-identical one-dimensional maps. Our primary focus is on finite invariant sets exhibiting ``toss-and-catch'' dynamics, in which trajectories alternate…
In the present work, a new time-dependent exchange theory is presented wherein the symmetry constraints, on a multi-electron wavefunction, are properly accounted for. In so doing, the equations of motion, incorporating the required…
We \emph{propose} a new \emph{invariant} for a \emph{cycle} of an \emph{interval map} $f:[0,1] \to [0,1]$, called its \emph{unfolding number}.
Bifurcations in a system of coupled maps are investigated. Using symbolic dynamics it is proven that for coupled shift maps the well known space--time--mixing attractor becomes unstable at a critical coupling strength in favour of a…
We examine energy and particle exchange between finite-sized quantum systems and find a new form of nonequilibrium states. The exchange rate undergoes stepwise evolution in time, and its magnitude and sign dramatically change according to…
In this paper, we consider chaotic dynamics and variational structures of area-preserving maps. There is a lot of study on dynamics of their maps and the works of Poincare and Birkhoff are well-known. To consider variational structures of…
Recently a generalization of shifts of finite type to the infinite alphabet case was proposed, in connection with the theory of ultragraph C*-algebras. In this work we characterize the class of continuous shift commuting maps between these…
We investigate a type of distance between triangulations on finite type surfaces where one moves between triangulations by performing simultaneous flips. We consider triangulations up to homeomorphism and our main results are upper bounds…
We consider the flip-width of geometric graphs, a notion of graph width recently introduced by Toru\'nczyk. We prove that many different types of geometric graphs have unbounded flip-width. These include interval graphs, permutation graphs,…
A translation surface is a surface formed by identifying edges of a collection of polygons in the complex plane that are parallel and of equal length using only translations. We determined that the same circle packing can be realized on…
We consider a class of discontinuous piecewise linear differential systems in $\mathbb{R}^3$ with two pieces separated by a plane. In this class we show that there exist differential systems having: a unique limit cycle, a unique…