Related papers: Non-uniform Cocycles for Some Uniquely Ergodic Min…
In this paper, an estimation of lower bound of topological entropy for coupled-expanding systems associated with transition matrices in compact Hausdorff spaces is given. Estimations of upper and lower bounds of topological entropy for…
Across all scales of the physical world, dynamical systems can often be usefully represented as abstract networks that encode the system's units and inter-unit interactions. Understanding how physical rules shape the topological structure…
We analyze the coherent dynamics of excitons in three dimensional topologically disordered networks with traps. If the interactions between the nodes of the network are long ranged, i.e., algebraically decaying as a function of the distance…
We consider discrete random dynamical systems induced by a non-elementary group action on a non-proper hyperbolic space. We prove that if the system is ergodic and satisfies the ``asymptotic past and future independence condition'' as…
The existence and uniqueness of weak solutions is shown for a system related to the Willis model of elastodynamics. Both the whole space case and the case of a bounded smooth domain are studied. To this end the equations are reformulated as…
We prove that the minimal chain recurrence classes of a holomorphic endomorphism of $\mathbb P^k$ have finitely many connected components. We also obtain results on arbitrary classes. These strong constraints on the topological dynamics in…
We characterize equicontinuous Delone dynamical systems as those coming from Delone sets with strongly almost periodic Dirac combs. Within the class of systems with nite local complexity the only equicontinuous systems are then shown to be…
Time-discrete dynamical systems on a finite state space have been used with great success to model natural and engineered systems such as biological networks, social networks, and engineered control systems. They have the advantage of being…
We construct symbolic dynamics on sets of full measure (w.r.t. an ergodic measure of positive entropy) for $C^{1+\epsilon}$ flows on compact smooth three-dimensional manifolds. One consequence is that the geodesic flow on the unit tangent…
In many sharing-economy applications, as well as in conventional economy applications, one wishes to regulate the behaviour of an ensemble of agents with guarantees on both the regulation of the ensemble in aggregate and the revenue or…
We begin development of a method for studying dynamical systems using concepts from computational complexity theory. We associate families of decision problems, called telic problems, to dynamical systems of a certain class. These decision…
We present a new solution for fundamental problems in nonlinear dynamical systems: finding, verifying, and stabilizing cycles. The solution we propose consists of a new control method based on mixing previous states of the system (or the…
We prove that a crossed product algebra arising from a minimal dynamical system on the product of the Cantor set and the circle has real rank zero if and only if that system is rigid. In the case that cocycles take values in the rotation…
We prove that the entropy map for countable Markov shifts of finite entropy is upper semi-continuous at ergodic measures. Note that the phase space is non-compact. Applications to systems that can be coded by these shifts, such as positive…
The current paper is devoted to the investigation of the influence of nested invariant cone structure on the dynamics, in the context of non-autonomous (time almost periodic)cases. We first prove that the nested invariant cone structure can…
Using the combinatorial properties of subsets of integers, a classification of metric dynamical systems was given in [V. Bergelson and T. Downarowicz, Large sets of integers and hierarchy of mixing properties of measure-preserving systems,…
We introduce and study two properties of dynamical systems: topologically transitive and topologically mixing under the set-valued setting. We prove some implications of these two topological properties for set-valued functions and…
In this paper we develop a systematic theory of compact operator semigroups on locally convex vector spaces. In particular we prove new and generalized versions of the mean ergodic theorem and apply them to different notions of mean…
A large class of technically non-chaotic systems, involving scatterings of light particles by flat surfaces with sharp boundaries, is nonetheless characterized by complex random looking motion in phase space. For these systems one may…
Under the assumption of the gluing orbit property, equivalent conditions to having zero topological entropy are investigated. In particular, we show that a dynamical system has the gluing orbit property and zero topological entropy if and…