Related papers: Affine interval exchange maps with a wandering int…
We studied topological and metric properties of the so-called interval translation maps (ITMs). For these maps, we introduced the maximal invariant measure and study its properties. Further, we study how the invariant measures depend on the…
We consider itinerant spinless fermions as moving defects in a dilute two-dimensional frustrated Ising system where they occupy site vacancies. Fermions interact via local spin fluctuations and we analyze coupled self-consistent mean-field…
We study affine maps between CAT(0) spaces with geometric actions, and show that they essentially split as products of dilations and linear maps (on the Euclidean factor). This extends known results from the Riemannian case. Furthermore, we…
We study an interval exchange transformation of [0,1] formed by cutting the interval at the points 1/n and reversing the order of the intervals. We find that the transformation is periodic away from a Cantor set of Hausdorff dimension zero.…
We study the complexity of the itineraries of injective piecewise contracting maps on the interval. We prove that for any such map the complexity function of any itinerary is eventually affine. We also prove that the growth rate of the…
Some skew-symmetrizable integer exchange matrices are associated to ideal (tagged) triangulations of marked bordered surfaces. These exchange matrices admits unfoldings to skew-symmetric matrices. We develop an combinatorial algorithm that…
We prove that any over-twist pattern is conjugate to an interval exchange transformation with bounded number of segments of isometry, restricted on one of its cycles. The bound is independent of the period and over-rotation number of the…
Characterisations of interval graphs, comparability graphs, co-comparability graphs, permutation graphs, and split graphs in terms of linear orderings of the vertex set are presented. As an application, it is proved that interval graphs,…
This paper studies the behavior under iteration of the maps T_{ab}(x,y) = (F_{ab}(x)- y, x) of the plane R^2, in which F_{ab}(x)= ax if x>0 and bx if x<0. These maps are area-preserving homeomorphisms of the plane that map rays from the…
We study the independence structure of finitely exchangeable distributions over random vectors and random networks. In particular, we provide necessary and sufficient conditions for an exchangeable vector so that its elements are completely…
In this note, continuous transitive maps $f$ on the interval $I$ are re-addressed, where $I$ denotes one of the intervals: $(-\infty, \infty)$, $(-\infty, a]$, $[b, \infty)$, $[a, b]$, where $a < b$ are real numbers. Such maps must have a…
This note presents an approach to studying the iterates of a mapping whose restriction to the complement of a finite set is continuous and open. The main examples to which the approach can be applied are piecewise monotone mappings defined…
An algorithm for calculating two-loop propagator type Feynman diagrams with arbitrary masses and external momentum is proposed. Recurrence relations allowing to express any scalar integral in terms of basic integrals are given. A minimal…
The exchange-degeneracy of the mesonic $f$, $\omega $, $\rho $ and $a_{2}$ Regge trajectories, dominant at moderate and high energies in hadron elastic scattering, is analyzed from two viewpoints. The first one concerns the masses of the…
We investigate the combinatorial and dynamical properties of so-called nearly Euclidean Thurston maps, or NET maps. These maps are perturbations of many-to-one folding maps of an affine two-sphere to itself. The close relationship between…
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…
A graph drawing in the plane is called an almost embedding if the images of any two non-adjacent simplices (i.e. vertices or edges) are disjoint. Almost embeddings (more precisely, their higher-dimensional analogues) naturally appear in…
The present work is concerned with characterizing some algebraic invariants of edge ideals of hypergraphs. To this aim, firstly, we introduce some kinds of combinatorial invariants similar to matching numbers for hypergraphs. Then we…
For a transitive countably piecewise monotone Markov interval map we consider the question whether there exists a conjugate map of constant slope. The answer varies depending on whether the map is continuous or only piecewise continuous,…
We examine maps between noncommutative projective spaces. A surjection of graded rings A-->A/J induces a closed immersion Proj(A/J)-->Proj(A). A homomorphism f:A-->B between graded rings induces an affine map U --> Proj(A) from a non-empty…