Related papers: Generic Dynamics on Compact Metric Spaces

We extend Teichmueller dynamics to a flow on the total space of a flat bundle of deformation spaces of representations of the fundamental group of a fixed surface S in a Lie group G. The resulting dynamical system is a continuous version of…

Living systems exhibit complex yet organized behavior on multiple spatiotemporal scales. To investigate the nature of multiscale coordination in living systems, one needs a meaningful and systematic way to quantify the complex dynamics, a…

Toric dynamical systems are known as complex balancing mass action systems in the mathematical chemistry literature, where many of their remarkable properties have been established. They include as special cases all deficiency zero systems…

This paper studies the behavior of dynamical systems in non-compact spaces, specifically focusing on the concepts of global attractors and shadowing. Let $K$ be a compact global attractor. We show that the shadowing property holds in…

We show that a minimal toplogical dynamical system that is frequently stable if and only if it is almost automorphic.

We establish connections between several properties of topological dynamical systems, such as: - every point is generic for an ergodic measure, - the map sending points to the measures they generate is continuous, - the system splits into…

Understanding the topology of the state space has proven to be extremely efficient for dynamical systems with a continuous state space. On the other hand, for particle systems on finite simple graphs, it has not yet been subject to deep…

In the following text we introduce specification property (stroboscopical property) for dynamical systems on uniform space. We focus on two classes of dynamical systems: generalized shifts and dynamical systems with Alexandroff…

We give a new short proof for the uniqueness of the universal minimal space. The proof holds for the uniqueness of the universal object in every collection of topological dynamical systems closed under taking projective limits and…

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,…

This is a survey on the local structure about a fixed point of discrete finite-dimensional holomorphic dynamical systems, discussing in particular the existence of local topological conjugacies to normal forms, and the structure of local…

By complexifying a Hamiltonian system one obtains dynamics on a holomorphic symplectic manifold. To invert this construction we present a theory of real forms which not only recovers the original system but also yields different real…

This note aims to bring attention to a simple class of discrete dynamical systems exhibiting some complex behaviour. Each of these systems is defined as a self-mapping of the unit square and is obtained by coupling two families of…

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,…

We study the dynamics of a coupled system, formed by a rigid body with a cavity entirely filled with magnetohydrodynamic compressible fluid. Our aim is to derive the global existence of the unique classical solutions and weak solutions to…

We investigate dynamical systems consisting of a locally compact Hausdorff space equipped with a partially defined local homeomorphism. Important examples of such systems include self-covering maps, one-sided shifts of finite type and, more…

We give a proof of the existence of generalized definable locally compact models for arbitrary approximate subgroups via an application of topological dynamics in model theory. Our construction is simpler and shorter than the original one…

We survey results on compact Clifford-Klein forms of homogeneous spaces, with a focus on recent contributions and organized around approaches via topology, geometry and dynamics. In addition, we survey results on moduli spaces of compact…

Topological signals, i.e., dynamical variables defined on nodes, links, triangles, etc. of higher-order networks, are attracting increasing attention. However the investigation of their collective phenomena is only at its infancy. Here we…

We prove that a topological contact isotopy uniquely defines a topological contact Hamiltonian. Combined with previous results from [MS11], this generalizes the classical one-to-one correspondence between smooth contact isotopies and their…