Related papers: Over-rotation numbers for unimodal maps
An interval translation map (ITM) is a map $T \colon I \to I$ defined as a piecewise translation on a finite partition of an interval $I$ into $r \ge 2$ subintervals. Unlike classical interval exchange transformations (IETs), the images of…
A corner in a map is an edge-vertex-edge triple consisting of two distinct edges incident to the same vertex. A corneration is a set of corners that covers every arc of the map exactly once. Cornerations in a dart-transitive map generalize…
Dynamical systems on the interval were widely studied because they are among the simplest systems and nevertheless they turn out to have complex dynamics. Many works on chaos were inspired by the behaviour of interval maps. However these…
Inspired by a twist maps theorem of Mather we study recurrent invariant sets that are ordered like rigid rotation under the action of the lift of a bimodal circle map $g$ to the $k$-fold cover. For each irrational in the interior of the…
We give upper and lower bounds on the spectral radius of a graph in terms of the number of walks. We generalize a number of known results.
This article introduces patterns of ideals of numerical semigroups, thereby unifying previous definitions of patterns of numerical semigroups. Several results of general interest are proved. More precisely, this article presents results on…
A novel effect of rotation in the optical image of structures in an opaque screen is presented. Theoretical calculations and experimental validation are presented. The features and the conditions of this effect are discussed.
We introduce smooth sequences of integral domains as well-ordered ascending chains that behave well at limit ordinals. Subsequently, we use this notion to give some conditions on the freeness of kernels of extension maps between groups of…
We present a method for computing the topological entropy of one-dimensional maps. As an approximation scheme, the algorithm converges rapidly and provides both upper and lower bounds.
Automorphisms of structural matrix algebras in block upper triangular form has been studied recently in \cite{Akkurt E-M Barker 2}, and this work is a follow-up paper of that study. The aim of this paper is to explain the topic in a much…
Subsurface projection has become indispensable in studying the geometry of the mapping class group and the curve complex of a surface. When the subsurface is an annulus, this projection is sometimes called relative twisting. We give two…
We survey recent developments on mapping class groups of surfaces of infinite topological type.
Given a unipotent bundle of smooth manifolds we construct its secondary transfer map and show that this map determines the higher smooth torsion of the bundle. This approach to higher torsion provides a new perspective on some of its…
In this paper we give a combinatorial description of the renormlization limits of infinitely renormalizable unimodal maps with {\it essentially bounded} combinatorics admitting quadratic-like complex extensions. As an application we…
A long-standing question is what invariant sets can be shared by two maps acting on the same space. A similar question stands for invariant measures. A particular interesting case are expanding Markov maps of the circle. If the two involved…
We address various notions of shadowing and expansivity for continuous maps restricted to a proper subset of their domain. We prove new equivalences of shadowing and expansive properties, we demonstrate under what conditions certain…
We study arrangements of intervals in $\mathbb{R}^2$ for which many pairs form trapezoids. We show that any set of intervals forming many trapezoids must have underlying algebraic structure, which we characterise. This leads to some…
We discuss the geometry of the c-map from projective special K\"ahler to quaternionic K\"ahler manifolds using the twist construction to provide a global approach to Hitchin's description. As found by Alexandrov et al. and Alekseevsky et…
We prove that for continuous maps on the interval, the existence of an n-cycle, implies the existence of n-1 points which interwind the original ones and are permuted by the map. We then use this combinatorial result to show that piecewise…
We study Schreier dynamical systems associated with a vast family of groups that hosts many known examples of groups of intermediate growth. We are interested in the orbital graphs for the actions of these groups on $d-$regular rooted trees…