Related papers: Topological Dynamics of Enveloping Semigroups

A convenient measure of a map or flow's chaotic action is the topological entropy. In many cases, the entropy has a homological origin: it is forced by the topology of the space. For example, in simple toral maps, the topological entropy is…

The notion of entropy appears in many fields and this paper is a survey about entropies in several branches of Mathematics. We are mainly concerned with the topological and the algebraic entropy in the context of continuous endomorphisms of…

Active emulsions and liquid crystalline shells are intriguing and experimentally realisable types of topological matter. Here we numerically study the morphology and spatiotemporal dynamics of a double emulsion, where one or two passive…

This paper investigates the dynamics of time-periodic Euler flows in multi-connected, planar fluid regions which are ``stirred'' by the moving boundaries. The classical Helmholtz theorem on the transport of vorticity implies that if the…

Topological dynamical systems $(X,T)$ are actions $T \times X \to X$, given as $(t, x) \to tx$, on a compact, Hausdorff topological space $X$ with $T$ as an acting group or monoid. We take up the property of topological transitivity…

Let $(X,T)$ be a topological dynamical system consisting of a compact metric space $X$ and a continuous surjective map $T : X \to X$. By using local entropy theory, we prove that $(X,T)$ has uniformly positive entropy if and only if so does…

In the Entropic Dynamics (ED) approach the essence of quantum theory lies in its probabilistic nature while the Hilbert space structure plays a secondary and ultimately optional role. The dynamics of probability distributions is driven by…

For topological dynamical systems $(X,T,\sigma)$ with abelian group $T$ which admit an equicontinuous factor $\pi:(X,T,\sigma)\to (Y,T,\delta)$ the Ellis semigroup $E(X)$ is an extension of $Y$ by its subsemigroup $E^{fib}(X)$ of elements…

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…

We investigate the $T\bar{T}$-like flows for non-linear electrodynamic theories in $D(=\!\!2n)$-dimensional spacetime. Our analysis is restricted to the deformation problem of the classical free action by employing the proposed $T\bar{T}$…

Flow networks are essential for both living organisms and enginneered systems. These networks often present complex dynamics controlled, at least in part, by their topology. Previous works have shown that topologically complex networks…

We analyse the topological (knot-theoretic) features of a certain codimension-one bifurcation of a partially hyperbolic fixed point in a flow on $\real^3$ originally described by Shil'nikov. By modifying how the invariant manifolds wrap…

In this expository paper we describe an unifying approach for many known entropies in Mathematics. First we recall the notion of semigroup entropy h_S in the category S of normed semigroups and contractive homomorphisms, recalling also its…

In the present work we consider the behavior of the geodesic flow on the unit tangent bundle of the 2-torus $T^2$ for an arbitrary Riemannian metric. A natural non-negative quantity which measures the complexity of the geodesic flow is the…

Let $X$ be a compact metric space and $T:X\longrightarrow X$ be continuous. Let $h^*(T)$ be the supremum of topological sequence entropies of $T$ over all subsequences of $\mathbb Z_+$ and $S(X)$ be the set of the values $h^*(T)$ for all…

We generalize the definition of topological entropy due to Adler, Konheim, and McAndrew \cite{AKM} to set-valued functions from a closed subset $A$ of the interval to closed subsets of the interval. We view these set-valued functions, via…

Hydrodynamic-like electron flows are typically modeled using the Stokes-Ohm equation or a kinetic description that is based on a dual-relaxation time approximation. Such models assume a short intrinsic mean free path $\ell_e$ due to…

A classical result of Schur of 1904 shows that an infinite (discrete) group $E$ with finite central quotient $E/Z(E)$ should have finite derived subgroup $[E,E]$. Schur's Theorem has many important consequences, which have been extensively…

In this work we introduce the notion of weak quasigroups, that are quasigroup operations defined almost everywhere on some set. Then we prove that the topological entropy and the ergodic period of an invertible expansive ergodically…

We consider discrete dynamical systems whose phase spaces are compact metrizable countable spaces. In the first part of the article, we study some properties that guarantee the continuity of all functions of the corresponding Ellis…