相关论文: Beyond primitivity for one-dimensional substitutio…
Robustness against small perturbations is a crucial feature of topological properties. This robustness is both a source of theoretical interest and a drive for technological applications, but presents a challenge when looking for new…
Torsion sensitive intersection homology was introduced to unify several versions of Poincare duality for stratified spaces into a single theorem. This unified duality theorem holds with ground coefficients in an arbitrary PID and with no…
We investigate the stability of maximizing measures for a penalty function of a two-dimensional subshift of finite type, building on the work of Gonschorowski et al. \cite{GQS}. In the one-dimensional case, such measures remain stable under…
We present theoretical and experimental results probing the rich topological structure of arbitrarily disordered finite tight binding Hamiltonians with chiral symmetry. We extend the known classification by considering the topological…
Primitive constant length substitutions generate minimal symbolic dynamical systems. In this article we present an algorithm which can produce the list of injective substitutions of the same length that generate topologically conjugate…
Multistable coupled map lattices typically support travelling fronts, separating two adjacent stable phases. We show how the existence of an invariant function describing the front profile, allows a reduction of the infinitely-dimensional…
We investigate the use of non-overlapping domain decomposition (DD) methods for nonlinear structure problems. The classic techniques would combine a global Newton solver with a linear DD solver for the tangent systems. We propose a…
We consider dynamical systems arising from substitutions over a finite alphabet. We prove that such a system is linearly repetitive if and only if it is minimal. Based on this characterization we extend various results from primitive…
The topological entropy dimension is mainly used to distinguish the zero topological entropy systems. Two types of topological entropy dimensions, the classical entropy dimension and the Pesin entropy dimension, are investigated for…
In the paper we study aperiodic substitutional dynamical systems arisen from non-primitive substitutions. We prove that the Vershik homeomorphism $\phi$ of a stationary ordered Bratteli diagram is homeomorphic to an aperiodic substitutional…
We present a general scheme how to construct a substitution rule for generating $d$-dimensional analogues of the paperfolding structures. This substitution is proven to be primitive, so that the translation action on the hull forms a…
We study multidimensional minimal and quasiperiodic shifts of finite type. We prove for these classes several results that were previously known for the shifts of finite type in general, without restriction. We show that some quasiperiodic…
In (2+1)-dimensional general relativity, the path integral for a manifold $M$ can be expressed in terms of a topological invariant, the Ray-Singer torsion of a flat bundle over $M$. For some manifolds, this makes an explicit computation of…
We prove that any unimodular Pisot substitution subshift is measurably conjugate to a domain exchange in an Euclidean space which is a finite topological extension of a translation on a torus.This generalizes the pioneer works of Rauzy and…
The first author's recent unexpected discovery of torsion in the integral cohomology of the T\"ubingen Triangle Tiling has led to a re-evaluation of current descriptions of and calculational methods for the topological invariants associated…
We elaborate on the interpretation of some mixed finite element spaces in terms of differential forms. First we develop a framework in which we show how tools from algebraic topology can be applied to the study of their cohomological…
The sublattice symmetry on a bipartite lattice is commonly regarded as the chiral symmetry in the AIII class of the tenfold Altland-Zirnbauer classification. Here, we reveal the spatial nature of sublattice symmetry, and show that this…
Non-Hermitian (NH) systems can display exceptional topological defects without Hermitian counterparts, exemplified by exceptional rings in NH two-dimensional systems. However, exceptional topological features associated with…
In this paper we characterize tame dynamical systems and functions in terms of eventual non-sensitivity and eventual fragmentability. As a notable application we obtain a neat characterization of tame subshifts $X \subset \{0,1\}^{\mathbb…
Here we shall consider the topology and dynamics associated to a wide class of matchbox manifolds, including a large selection of tiling spaces and all minimal matchbox manifolds of dimension one. For such spaces we introduce topological…