Related papers: Nilsequences and a structure theorem for topologic…
The thermodynamic definition of entropy can be extended to nonequilibrium systems based on its relation to information. To apply this definition in practice requires access to the physical system's microstates, which may be prohibitively…
Recurrence is a fundamental characteristic of dynamical systems with complicated behavior. Understanding the inner structure of recurrence is challenging, especially if the system has many degrees of freedom and is subject to noise. We…
For a topological dynamical system $(X, T)$, $l\in\mathbb{N}$ and $x\in X$, let $N_l(X)$ and $L_x^l(X)$ be the orbit closures of the diagonal point $(x,x,\ldots,x)$ ($l $ times) under the actions $\mathcal{G}_{l}$ and $\tau_l $…
Inferring network topology from dynamical observations is a fundamental problem pervading research on complex systems. Here, we present a simple, direct method to infer the structural connection topology of a network, given an observation…
Chaotic attractors, chaotic saddles and periodic orbits are examples of chain-recurrent sets. Using arbitrary small controls, a trajectory starting from any point in a chain-recurrent set can be steered to any other in that set. The…
We define weaker forms of topological and measure theoretical equicontinuity for topological dynamical systems and we study their relationships with systems with discrete spectrum and zero sequence entropy. In the topological category we…
Modeling a sequence of design steps, or a sequence of parameter settings, yields a sequence of dynamical systems. In many cases, such a sequence is intended to approximate a certain limit case. However, formally defining that limit turns…
Fast and accurate structural dynamics analysis is important for structural design and damage assessment. Structural dynamics analysis leveraging machine learning techniques has become a popular research focus in recent years. Although the…
This paper introduces indefinite proximities inherent in the collection of physical objects found in a dynamical system. Axiomatically, these indefinite proximities lead to a new form of Hausdorff topology, which is indefinite…
Networks are universally considered as complex structures of interactions of large multi-component systems. In order to determine the role that each node has inside a complex network, several centrality measures have been developed. Such…
In this paper, we systematically investigate the nilpotentizer and nilpotent graph for a Lie superalgebra over the field of characteristic not equal to 2. First, we establish some fundamental properties of the nilpotentizer. Next, we show…
Nilsequences arose in the study of the multiple ergodic averages associated to Furstenberg's proof of Szemer\'edi's Theorem and have since played a role in problems in additive combinatorics. Nilsequences are a generalization of almost…
In this paper we provide explicit dual Ramsey statements for several classes of finite relational structures (such as finite linearly ordered graphs, finite linearly ordered metric spaces and finite posets with a linear extension) and…
We study dynamical systems forced by a combination of random and deterministic noise and provide criteria, in terms of Lyapunov exponents, for the existence of random attractors with continuous structure in the fibres. For this purpose, we…
Cocycles are a key object in Antol\'{i}n Camarena and Szegedy's (topological) theory of nilspaces. We introduce measurable counterparts, named nilcycles, enabling us to give conditions which guarantee that an ergodic group extension of a…
In this paper we study a class of physical systems that combine a finite number of mechanical and thermodynamic observables. We call them finite dimensional thermo-mechanical systems. We introduce these systems by means of simple examples.…
We introduce structural heterogeneity, a new topological characteristic for semi-ordered materials that captures their degree of organisation at a mesoscopic level and tracks their time-evolution, ultimately detecting the order-disorder…
We discuss the application of various concepts from the theory of topological dynamical systems to Delone sets and tilings. We consider in particular, the maximal equicontinuous factor of a Delone dynamical system, the proximality relation…
A computation of the dynamical structure factor of topologically disordered systems, where the disorder can be described in terms of euclidean random matrices, is presented. Among others, structural glasses and supercooled liquids belong to…
A theory of structure is formulated for systems of many structureless classical particles with stable local interactions in Euclidean space. Such systems are shown to have their structure in thermodynamic equilibrium determined exactly by a…