Related papers: Different Statistical Behaviors of Orbits

A sofic approximation to a countable group is a sequence of partial actions on finite sets that asymptotically approximates the action of the group on itself by left-translations. A group is sofic if it admits a sofic approximation. Sofic…

We study (topological) pseudo-Anosov flows from the perspective of the associated group actions on their orbit spaces and boundary at infinity. We extend the definition of Anosov-like action from [BFM22] from the transitive to the general…

In this paper, we study dynamics of maps on quasi-graphs characterizing their invariant measures. In particular, we prove that every invariant measure of quasi-graph map with zero topological entropy has discrete spectrum. Additionally, we…

Coarse geometry studies metric spaces on the large scale. Our goal here is to study dynamics from a coarse point of view. To this end we introduce a coarse version of topological entropy, suitable for unbounded metric spaces, consistent…

We study the dynamics of discrete-time regulatory networks on random digraphs. For this we define ensembles of deterministic orbits of random regulatory networks, and introduce some statistical indicators related to the long-term dynamics…

Topological invariants have proved useful for analyzing emergent function as they characterize a property of the entire system, and are insensitive to local details, disorder, and noise. They support boundary states, which reduce the system…

Statistical Topology emerged since topological aspects continue to gain importance in many areas of physics. It is most desirable to study topological invariants and their statistics in schematic models that facilitate the identification of…

The excitation spectrum of the one-dimensional spin-orbital model in a magnetic field is studied, using a recently developed dynamical density matrix renormalization group technique. The method is employed on chains with up to 80 sites, and…

In the study of discrete dynamical systems, we typically start with a function from a space into itself, and ask questions about the properties of sequences of iterates of the function. In this paper we reverse the direction of this study.…

We characterize and describe the extensions of expansive and Anosov homeomorphisms on compact spaces. As an application we obtain a stability result for extensions of Anosov systems, and show a construction that embeds any expansive system…

Dynamics arising persistently in smooth dynamical systems ranges from regular dynamics (periodic, quasiperiodic) to strongly chaotic dynamics (Anosov, uniformly hyperbolic, nonuniformly hyperbolic modelled by Young towers). The latter…

We study relations between transitivity, mixing and periodic points on dendrites. We prove that when there is a point with dense orbit which is not an endpoint, then periodic points are dense and there is a terminal periodic decomposition…

Traditionally, robots are regarded as universal motion generation machines. They are designed mainly by kinematics considerations while the desired dynamics is imposed by strong actuators and high-rate control loops. As an alternative, one…

We investigate the location and structure of the Birkhoff center for competitive dynamical systems, and give a comprehensive description of recurrence and statistical behavior of orbits. An order-structure dichotomy is established for any…

For spatiotemporal chaos described by partial differential equations, there are generally locations where the dynamical variable achieves its local extremum or where the time partial derivative of the variable vanishes instantaneously. To a…

In this article, we investigate the convergence behavior of two classes of gathering protocols with fixed circulant topologies using tools from dynamical systems. Given a fixed number of mobile entities moving in the Euclidean plane, we…

We study the behaviour at tipping points close to (smoothed) non-smooth fold bifurcations in one-dimensional oscillatory forced systems. The focus is the Stommel-Box, and related climate models, which are piecewise-smooth continuous…

We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…

We study the amount of nonhyperbolicity within a broad class of (nonhyperbolic) partially hyperbolic diffeomorphisms with a one-dimensional center. For that, we focus on the center Lyapunov exponent and the entropy of its level sets. We…

We study the distribution of maxima (Extreme Value Statistics) for sequences of observables computed along orbits generated by random transformations. The underlying, deterministic, dynamical system can be regular or chaotic. In the former…