相关论文: Topological Bragg Peaks And How They Characterise …

It is well-known that the dynamical spectrum of an ergodic measure dynamical system is related to the diffraction measure of a typical element of the system. This situation includes ergodic subshifts from symbolic dynamics as well as…

We propose a new way of thinking about one parameter persistence. We believe topological persistence is fundamentally not about decomposition theorems but a central role is played by a choice of metrics. Choosing a pseudometric between…

We give a new approach to the study of statistical mechanical systems: algebraic topology is used to investigate the statistical distributions of stochastic currents generated in graphs. In the adiabatic and low temperature limits we will…

Topological phases of matter are often understood and predicted with the help of crystal symmetries, although they don't rely on them to exist. In this chapter we review how topological phases have been recently shown to emerge in amorphous…

A probability measure is a characteristic measure of a topological dynamical system if it is invariant to the automorphism group of the system. We show that zero entropy shifts always admit characteristic measures. We use similar techniques…

Topological order in two-dimensional systems is studied by combining the braid group formalism with a gauge invariance analysis. We show that flux insertions (or large gauge transformations) pertinent to the toroidal topology induce…

We present a graph theory-based method to characterise flow defects and structural shifts in condensed matter. We explore the connection between dynamical properties, particularly the recently introduced concept of ''softness'', and…

A paradigmatic nonhyperbolic dynamical system exhibiting deterministic diffusion is the smooth nonlinear climbing sine map. We find that this map generates fractal hierarchies of normal and anomalous diffusive regions as functions of the…

This paper is second in the series, following Pranav et al. (2019), focused on the characterization of geometric and topological properties of 3D Gaussian random fields. We focus on the formalism of persistent homology, the mainstay of…

The photonic band dispersion and density of states (DOS) are calculated for the three-dimensional (3D) hexagonal structure corresponding to a distributed Bragg reflector patterned with a 2D triangular lattice of circular holes. Results for…

In this survey we describe how the so-called Dold congruence arises in topology, and how it relates to periodic point counting in dynamical systems.

We use the first Betti number of a complex to characterize the morphological structure of granular samples in mechanical equilibrium. We analyze two-dimensional granular packings after a tapping process by means of both simulations and…

We provide a framework for studying randomly coloured point sets in a locally compact, second-countable space on which a metrisable unimodular group acts continuously and properly. We first construct and describe an appropriate dynamical…

One way to characterize configurations of points up to congruence is by considering the distribution of all mutual distances between points. This paper deals with the question if point configurations are uniquely determined by this…

Topological data analysis (TDA), while abstract, allows a characterization of time-series data obtained from nonlinear and complex dynamical systems. Though it is surprising that such an abstract measure of structure - counting pieces and…

A nonlinearly coupled system of bouncing balls is shown to exhibit features like self-organised-criticality (SOC) and punctuated equilibrium (PE) in suitable parameter domains. The temporal evolution of the non-stationary amplitudes is…

From the topological properties of a three dimensional vector order parameter, the topological current of point defects is obtained. One shows that the charge of point defects is determined by Hopf indices and Brouwer degrees. The evolution…

In the band theory for non-Hermitian systems, the energy eigenvalues, which are complex, can exhibit non-trivial topology which is not present in Hermitian systems. In one dimension, it was recently noted theoretically and demonstrated…

The periodic points of a morphism of good reduction for a smooth projective curve with good reduction over the p-adics form a discrete set. This is used to give an interpretation of the morphic height in terms of asymptotic properties of…

We consider measurable and topological dynamical systems over locally compact abelian groups. Our main observation relates convergence of Wiener-Wintner type averages to eigenvalues of the dynamical system in question. As a consequence we…