Related papers: Interval exchanges that do not embed in free group…

We present a computational study of finite-time mixing of a line segment by cutting and shuffling. A family of one-dimensional interval exchange transformations is constructed as a model system in which to study these types of mixing…

In this paper, we study the structure of the permutability graphs of subgroups, and the permutability graphs of non-normal subgroups of the following groups: the dihedral groups $D_n$, the generalized quaternion groups $Q_n$, the…

The distributive property can be studied through bilinear maps and various morphisms between these maps. The adjoint-morphisms between bilinear maps establish a complete abelian category with projectives and admits a duality. Thus the…

We establish conditions for the existence of a family of piecewise linear invariant curves in a two-parameter family of piecewise isometries on the upper half-plane known as Translated Cone Exchange Transformations. We show that these…

We show that a group of diffeomorphisms $\D$ on the open unit interval $I,$ equipped with the topology of uniform convergence on any compact set of the derivatives at any order, is non regular: the exponential map is not defined for some…

Let $\mathcal{R}$ be a $2$-torsion free commutative ring with unity, $X$ a locally finite pre-ordered set and $I(X,\mathcal{R})$ the incidence algebra of $X$ over $\mathcal{R}$. If $X$ consists of a finite number of connected components, in…

We introduce a definition of admissibility for subintervals in interval exchange transformations. Using this notion, we prove a property of the natural codings of interval exchange transformations, namely that any derived set of a regular…

We show that there exists an interval exchange and a point so that the orbit of the point equidistributes for a measure that is not ergodic.

We investigate the dynamics of a generic interacting many-body system under conditions of electromagnetically induced transparency (EIT). This problem is of current relevance due to its connection to non-linear optical media realized by…

Directed graphs occur throughout statistical modeling of networks, and exchangeability is a natural assumption when the ordering of vertices does not matter. There is a deep structural theory for exchangeable undirected graphs, which…

Here the Integral Value Transformations (IVTs) are considered to be Discrete Dynamical System map in the space\mathbb{N}_(0). In this paper, the dynamics of IVTs is deciphered through the light of Topological Dynamics.

We investigate the computational complexity of finding temporally disjoint paths or walks in temporal graphs. There, the edge set changes over discrete time steps and a temporal path (resp. walk) uses edges that appear at monotonically…

We classify the locally finite ergodic invariant measures of certain infinite interval exchange transformations (IETs). These transformations naturally arise from return maps of the straight-line flow on certain translation surfaces, and…

Let $G$ be a locally compact group. A random closed subgroup with conjugation-invariant law is called an {\em invariant random subgroup} or IRS for short. We show that each nonabelian free group has a large "zoo" of IRS's. This contrasts…

Let G be an abelian group and let lambda be the smallest rank of any group whose direct sum with a free group is isomorphic to G. If lambda is uncountable, then G has lambda pairwise disjoint, non-free subgroups. There is an example where…

In this article we provide sufficient conditions on a self-similar interval exchange map, whose renormalization matrix has complex eigenvalues of modulus greater than one, for the existence of affine interval exchange maps with wandering…

For a continuous map on the unit interval or circle, we define the bifurcation set to be the collection of those interval holes whose surviving set is sensitive to arbitrarily small changes of their position. By assuming a global…

In this paper we prove the existence of minimal non uniquely ergodic flipped IETs. In particular, we build explicitly minimal non uniquely ergodic $(10,k)$-IETs for any $1\leq k \leq 10$. This answers an open question posed in…

We introduce a mathematical framework for symmetry-resolved entanglement entropy with a non-abelian symmetry group. To obtain a reduced density matrix that is block-diagonal in the non-abelian charges, we define subsystems operationally in…

In this work, we introduce the \emph{interval permutation segment (IP-SEG)} model that naturally generalizes the geometric intersection models of interval and permutation graphs. We study properties of two graph classes that arise from the…