Related papers: Reconstructing a minimal topological dynamical sys…
The dynamics of finite dimension open quantum systems is studied with the help of the simplest possible form of projection operators, namely the ones which project only onto one dimensional subspaces. The simplicity of the action of the…
We study non-recurrence sets for weakly mixing dynamical systems by using linear dynamical systems. These are systems consisting of a bounded linear operator acting on a separable complex Banach space X, which becomes a probability space…
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused…
We propose a topological approach suitable to establish a connection between thermodynamics and topology in the microcanonical ensemble. Indeed, we report on results that point to the possibility of describing {\it interacting classical…
In this paper we study topological cocycles for minimal homeomorphisms on a compact metric space. We introduce a notion of an essential range for topological cocycles with values in a locally compact group, and we show that this notion…
This paper is a first step in the study of the recurrence behavior in random dynamical systems and randomly perturbed dynamical systems. In particular we define a concept of quenched and annealed return times for systems generated by the…
Recurrence determinism, one of the fundamental characteristics of recurrence quantification analysis, measures predictability of a trajectory of a dynamical system. It is tightly connected with the conditional probability that, given a…
We consider random walks in which the walk originates in one set of nodes and then continues until it reaches one or more nodes in a target set. The time required for the walk to reach the target set is of interest in understanding the…
We construct a microscopic model to study discrete randomness in bistable systems coupled to an environment comprising many degrees of freedom. A quartic double well is bilinearly coupled to a finite number $N$ of harmonic oscillators.…
Simple examples are used to introduce and examine symmetries of open quantum dynamics that can be described by unitary operators. For the Hamiltonian dynamics of an entire closed system, the symmetry takes the expected form which, when the…
The paper deals with the problem of reconstructing the topological structure of a network of dynamical systems. A distance function is defined in order to evaluate the "closeness" of two processes and a few useful mathematical properties…
We investigate the dynamics of a binary mixture Lennard-Jones system of different system sizes with respect to the importance of the properties of the underlying potential energy landscape (PEL). We show that the dynamics of small systems…
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…
We continue our study of the fractal structure of escape-time plots for chaotic maps. In the preceding paper, we showed that the escape-time plot contains regular sequences of successive escape segments, called epistrophes, which converge…
The main result of this paper is an analogue for a continuous family of tori of Kronecker-Weyl's unique ergodicity of irrational rotations. We show that the notion corresponding in this setup to irrationality, namely asynchronicity, is…
We show that the standard Hamiltonian of isotropic loop quantum cosmology is selected by physical criteria plus one choice: that it have a `minimal' number of terms. We also show the freedom, and boundedness of energy density, even when…
Over the past few years, topological insulators have taken center stage in solid state physics. The desire to tune the topological invariants of the bulk and thus control the number of edge states has steered theorists and experimentalists…
Some basic notions and results in Topological Dynamics are extended to continuous groupoid actions in topological spaces. We focus mainly on recurrence properties. Besides results that are analogous to the classical case of group actions,…
In this paper, we study the polyhedral structure of an integrated minimum-up/-down time and ramping polytope, which has broad applications in variant industries. The polytope we studied includes minimum-up/-down time, generation…
The problem of linking the structure of a finite linear dynamical system with its dynamics is well understood when the phase space is a vector space over a finite field. The cycle structure of such a system can be described by the…