Related papers: Dynamical systems, simulation, abstract computatio…
An overview of dynamical systems in accelerator physics is presented with a suggestion of a few issues to be addressed. Also mentioned are a few possible developments in the future. Technical details supporting the views are not presented.
We study random dynamical systems of certain continuous functions on the unit interval. We use bounded variation to provide sufficient conditions for unique ergodicity of these systems. Several classes of examples are provided.
The goal of this work is to study the space of continuous functions whose ergodic averages converge everywhere towards a continuous function. We will connect, as in the case of a metric study, the convergence of the ergodic averages and the…
Dynamics, the study of change, is normally the subject of mechanics. Whether the chosen mechanics is ``fundamental'' and deterministic or ``phenomenological'' and stochastic, all changes are described relative to an external time. Here we…
The complex dynamics of physical systems can often be modeled with stochastic differential equations. However, computational constraints inhibit the estimation of dynamics from large time-series datasets. I present a method for estimating…
We present some new results which relate information to chaotic dynamics. In our approach the quantity of information is measured by the Algorithmic Information Content (Kolmogorov complexity) or by a sort of computable version of it…
The problem of characterizing complexity of quantum dynamics - in particular of locally interacting chains of quantum particles - will be reviewed and discussed from several different perspectives: (i) stability of motion against external…
The topic of statistical inference for dynamical systems has been studied extensively across several fields. In this survey we focus on the problem of parameter estimation for non-linear dynamical systems. Our objective is to place results…
Like with most large-scale systems, the evaluation of quantitative properties of collective adaptive systems is an important issue that crosscuts all its development stages, from design (in the case of engineered systems) to runtime…
In this expository and resources chapter we review selected aspects of the mathematics of dynamical systems, stability, and chaos, within a historical framework that draws together two threads of its early development: celestial mechanics…
We discuss some classical and recent results and open problems on the statistical behavior of ergodic sums above toral translations, and their applications to Diophantine approximations and to ergodic properties of systems related to…
This paper presents a survey of recent and not so recent results concerning the study of smooth homeomorphisms of the circle with a finite number of non-flat critical points, an important topic in the area of One-dimensional Dynamics. We…
The use of statistical methods to model gravitational systems is crucial to physics practice, but the extent to which thermodynamics and statistical mechanics genuinely apply to these systems is a contentious issue. This paper provides new…
This paper gives an introduction to \textit{Cognidynamics}, that is to the dynamics of cognitive systems driven by optimal objectives imposed over time when they interact either with a defined virtual or with a real-world environment. The…
It is notoriously difficult to apply statistical mechanics to generally covariant systems, because the notions of time, energy and equilibrium are seriously modified in this context. We discuss the conditions under which weaker versions of…
Straight lines are common features in human made environments, which makes them a frequently explored feature for control applications. Many control schemes, like Visual Servoing, require the 3D parameters of the features to be estimated.…
How chaos is useful in the brain information processing is greatly unknown. Here, we show that the statistical property of chaos such as invariant measures naturally organized under a great number of iterations of chaotic mappings can be…
We introduce the concepts of Baire Ergodicity and Ergodic Formalism, employing them to study topological and statistical attractors. Specifically, we establish the existence and finiteness of such attractors and provide applications for…
Dynamical equations describing physical systems at statistical equilibrium are commonly extended by mathematical tools called "thermostats". These tools are designed for sampling ensembles of statistical mechanics. We propose a dynamic…
Dynamical systems are ubiquitous in science and engineering as models of phenomena that evolve over time. Although complex dynamical systems tend to have important modular structure, conventional modeling approaches suppress this structure.…