Related papers: Transitive mappings on the Cantor fan

The resistance of layered conductors with a multisheet Fermi surface (FS), in a high magnetic field, in the immediate vicinity of Lifshic's topological transition when the separate FS sheets are drown together by an external action,…

A new class of multilayered functional materials has recently emerged in which the component atomic layers are held together by weak van der Waals forces that preserve the structural integrity and physical properties of each layer. An…

In this work, we investigate the classical loop models doped with monomers and dimers on a square lattice, whose partition function can be expressed as a tensor network (TN). In the thermodynamic limit, we use the boundary matrix product…

The possibility of topological phase transition with or without a magnetic flux trapped in the cells of a class of decorated lattices is explored in details.Using a tight binding Hamiltonian and a real space decimation scheme we…

A homeomorphism f of a manifold M is called H_1-transitive if there is a transitive lift of an iterate of f to the universal Abelian cover \tM. Roughly speaking, this means that f has orbits which repeatedly and densely explore all elements…

This paper is a survey devoted to the study of probability and infinite ergodic invariant measures for aperiodic homeomorphisms of a Cantor set. We focus mostly on the cases when a homeomorphism has either a unique ergodic invariant measure…

We consider multi-terminal transport through a flake of rectangular shape of a two-dimensional topological insulator in the presence of an in-plane magnetic field. This system has been shown to be a second-order topological insulator, thus…

We show that a non-wandering endomorphism of the torus with invertible linear part without invariant directions and for which the critical points are in some sense generic is transitive. This improves a result of Andersson by allowing…

Graphene was the first material predicted to be a time-reversal-invariant topological insulator; however, the insulating gap is immeasurably small owing to the weakness of spin-orbit interactions in graphene. A recent experiment [1]…

We derive a necessary and sufficient condition for a homeomorphism with the shadowing property to be topologically transitive: to have an invariant subset $A$, dense in the non-wandering set, where the barycenter property holds. To…

The purpose of this article is to develop foundational techniques from logarithmic geometry in order to define a functorial tropicalization map for fine and saturated logarithmic schemes in the case of constant coefficients. Our approach…

The topological mechanics is a perfect tool that can bridge the gap between the quantum and Newtonian physics and mechanics of materials. It requires discrete models of the material with analogies with the topological characteristics of…

Moment-angle manifolds provide a wide class of examples of non-Kaehler compact complex manifolds. A complex moment-angle manifold Z is constructed via certain combinatorial data, called a complete simplicial fan. In the case of rational…

In the first part of this text we give a survey of the properties satisfied by the C1-generic conservative diffeomorphisms of compact surfaces. The main result that we will discuss is that a C1-generic conservative diffeomorphism of a…

Since the thermal conduction equation has form invariance under coordinate transformation, one can design thermal metamaterials with novel functions by tailoring materials' thermal conductivities. In this work, we establish a different…

A salient feature of topological phases are surface states and many of the widely studied physical properties are directly tied to their existence. Although less explored, a variety of topological phases can however similarly be…

Topological insulators are materials where current does not flow through the bulk, but along the boundaries, only. They are of particular practical importance, since it is considerably more difficult, by ``conventional'' means, to affect…

In the article "Construction of the continuous hull for the combinatorics of a regular pentagonal tiling of the plane" we constructed a compact topological space for the combinatorics of "A regular pentagonal tiling of the plane", which we…

In this paper we present a systematic study of continuous local iterated function systems. We prove local iterated function systems admit compact attractors and, under a contractivity assumption, construct their code space and present an…

We study the dynamics of measurable pseudo-Anosov homeomorphisms of surfaces, a generalization of Thurston's pseudo-Anosov homeomorphisms. A measurable pseudo-Anosov map has a transverse pair of full measure turbulations consisting of…