Related papers: Switched flow systems: pseudo billiard dynamics
We introduce a geometric dynamical system where iteration is defined as a cycling composition of different maps acting on a space composed of three or more lines in $\mathbb{R}^2$. This system is motivated by the dynamics of iterated…
Inspired by the work of Pujals and Sambarino on dominated splitting, we present billiards with a modified reflection law which constitute simple examples of dynamical systems with limit sets with dominated splitting and where the dynamics…
We study chaotic properties of eigenstates depending on the degree of complexity in boundaries of a 2D periodic billiard. Main attention is paid to the situation when the motion of a classical particle is strongly chaotic. Our approach…
Experiments with superconducting microwave cavities have been performed in our laboratory for more than two decades. The purpose of the present article is to recapitulate some of the highlights achieved. We briefly review (i) results…
Many casinos routinely use mechanical card shuffling machines. We were asked to evaluate a new product, a shelf shuffler. This leads to new probability, new combinatorics and to some practical advice which was adopted by the manufacturer.…
Considering a quantized chaotic system, we analyze the evolution of its eigenstates as a result of varying a control parameter. As the induced perturbation becomes larger, there is a crossover from a perturbative to a non-perturbative…
We study a control system resembling a singularly perturbed system whose variables are decomposed into groups that change their values with rates of different orders of magnitude. We establish that the slow trajectories of this system are…
Semiconductor billiards are often considered as ideal systems for studying dynamical chaos in the quantum mechanical limit. In the traditional picture, once the electron's mean free path, as determined by the mobility, becomes larger than…
The theory of complex networks and of disordered systems is used to study the stability and dynamical properties of a simple model of material flow networks defined on random graphs. In particular we address instabilities that are…
Level dynamics measurements have been performed in a Sinai microwave billiard as a function of a single length, as well as in rectangular billiards with randomly distributed disks as a function of the position of one disk. In the first case…
As tools for dynamic system modelling both conventional methods such as transfer function or state space representation and modern power flow based methods are available. The latter methods do not depend on energy domain, are able to…
The dynamics by iteration of a function on a compact metric space, sometimes called a cascade, can be extended to the dynamics of a closed relation on such a space. Here we apply this relation dynamics to study semiflows (and their relation…
The control properties of discrete-time switched linear systems (SLS) with switching signals generated by logical dynamic systems are studied using the semi-tensor product (STP) approach. With the algebraic state space representation…
We give a beautiful explicit example of a convex plane curve such that the outer billiard has a given finite number of invariant curves. Moreover, the dynamics on these curves is a standard shift. This example can be considered as an outer…
Electronics has changed greatly during recent decades, and some its basic concepts should be revisited. Starting from the sampling procedure, we consider some mathematical, physical and engineering aspects related to singular, mainly…
We study the dynamics of one-particle and few-particle billiard systems in containers of various shapes. In few-particle systems, the particles collide elastically both against the boundary and against each other. In the one-particle case,…
This paper examines a continuous time dynamical system that is an extension of a discrete time dynamical system previously examined, and considers this system together in a product space with a compact subset of Euclidean space. Together,…
Looped-functionals have been shown to be relevant for the analysis of a wide variety of systems. However, the conditions obtained in previous works on the analysis of sampled-data, impulsive and switched systems have only been shown to be…
A universal theory of linear instabilities in swirling flows, occurring in both natural settings and industrial applications, is formulated. The theory encompasses a wide range of open and confined flows, including spiral isothermal flows…
We prove some partial results on the periodicity of billiard systems on graphs. The results specialize to the case of $n$ billiards with equal mass on the unit interval or circle traveling at the same speed.