相关论文: There exists a topologically mixing IET

We study the topological entropy of hom tree-shifts and show that, although the topological entropy is not a conjugacy invariant for tree-shifts in general, it remains invariant for hom tree higher block shifts. In…

This note is to concern a generalization to the case of twisted coefficients of the classical theory of Abelian differentials on a compact Riemann surface. We apply the Dirichlet's principle to a modified energy functional to show the…

The purpose of this note is to present my understanding of Tim Austin's proof of the multiple ergodic theorem for commuting transformations, emphasizing on the use of joinings, extensions and factors. The existence of a sated extension,…

We consider the existence of the topological entropy of shift spaces on a finitely generated semigroup whose Cayley graph is a tree. The considered semigroups include free groups. On the other hand, the notion of stem entropy is introduced.…

We show that every transformation is disjoint from almost every interval exchange transformation (IET), answering a question of Bufetov. In particular, we prove that almost every pair of IETs is disjoint. It follows that the product of…

Extensive amenability is a property of group actions which has recently been used as a tool to prove amenability of groups. We study this property and prove that it is preserved under a very general construction of semidirect products. As…

A rotated odometer is an infinite interval exchange transformation (IET) obtained as a composition of the von Neumann-Kakutani map and a finite IET of intervals of equal length. In this paper, we consider rotated odometers for which the…

We give a homological construction of aperiodic tiles for certain open Riemannian surfaces admitting actions of Grigorchuk groups of intermediate growth.

In this thesis, we provide an initial investigation into bounds for topological entropy of switched linear systems. Entropy measures, roughly, the information needed to describe the behavior of a system with finite precision on finite time…

We describe various strengthenings of the concept of topological transitivity. Especially when one departs from the family of invertible systems, a number of interesting properties arise. We present the architecture of implications among…

The term "overlapping" refers to a certain fairly simple type of piecewise continuous function from the unit interval to itself and also to a fairly simple type of iterated function system (IFS) on the unit interval. A correspondence…

We show that a typical interval exchange transformation is either weakly mixing or it is an irrational rotation. We also conclude that a typical translation flow on a surface of genus $g \geq 2$ (with prescribed singularity types) is weakly…

Motivated by link transformations of lattice gauge theory, a method for generating local unitary invariants, especially for a system of qubits, has been pointed out in an earlier work [M. S. Williamson {\it et. al.}, Phys. Rev. A {\bf 83},…

We study etale extensions of rings that have FIP.

Topological insulators (TIs) are bulk insulators with exotic 'topologically protected' surface conducting modes. It has recently been pointed out that when stacked together, interactions between surface modes can induce diverse phases…

Topological phase transitions involving crystalline symmetry breaking provide a fertile ground to explore the interplay between symmetry, topology, and emergent quantum phenomena. Recently discovered quasi-one-dimensional topological…

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 discuss different properties and the ability of several topological invariants based on position operators to identify phase transitions, and compare with more accurate methods, like crossing of excited energy levels and jumps in Berry…

The electromagnetically induced transparency (EIT) phenomenon in a four level atomic system with tripod configuration is studied. The results show that this configuration is equivalent to the combination of two single three-level $\Lambda$…

A criterion for unique ergodicity for points of a curve in the space of interval exchange transformation is given.