Related papers: Topological entropy of nonautonomous dynamical sys…

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…

Two general upper bounds on the topological entropy of nonlinear time-varying systems are established: one using the matrix measure of the system Jacobian, the other using the largest real part of the eigenvalues of the Jacobian matrix with…

In this paper, we study the topological entropy and the Hausdorff dimension of a shrinking target set. We give lower and upper bounds of topological entropy and Hausdorff dimension for dynamical systems with exponential specification…

It is proved that whenever a zero entropy dynamical system $(X,T)$ has only countably many ergodic measures and $\mu$ stands for the arithmetic M{\"o}bius function, then there exists a subset $A$ of integers depending only on the system, of…

Topological measures and deficient topological measures generalize Borel measures and correspond to certain non-linear functionals. We study integration with respect to deficient topological measures on locally compact spaces. Such an…

We use the complexity function of an invariant, not necessary closed, subset of a two-sided shift space to compute the polynomial entropy of the induced dynamics on the hyperspace of continua for certain one-dimensional dynamical systems.…

The theoretical and numerical understanding of the key concept of topological entropy is an important problem in dynamical systems. Most studies have been carried out on maps (discrete-time systems). We analyse a scenario of global changes…

Let $f:M\rightarrow M$ be a $C^1$ diffeomorphism with a dominated splitting on a compact Riemanian manifold $M$ without boundary. We state and prove several sufficient conditions for the topological entropy of $f$ to be positive. The…

Pfister and Sullivan proved that if a topological dynamical system $(X,T)$ satisfies almost product property and uniform separation property, then for each nonempty compact %convex subset $K$ of invariant measures, the entropy of saturated…

In this work, we show that if $f$ is a uniformly continuous map defined over a Polish metric space, then the set of $f$-invariant measures with zero metric entropy is a $G_\delta$ set (in the weak topology). In particular, this set is…

We study the directional entropy of the dynamical system associated to a $\Z^2$ configuration in a finite alphabet. We show that under local assumptions on the complexity, either every direction has zero topological entropy or some…

Given a partially hyperbolic diffeomorphism $f:M \rightarrow M$ defined on a compact Riemannian manifold $M$, in this paper we define the concept of unstable topological entropy of $f$ on a set $Y \subset M$ not necessarily compact and we…

We show vanishing results about the infimum of the topological entropy of the geodesic flow of homogeneous smooth four manifolds. We prove that any closed oriented geometric four manifold has zero minimal entropy if and only if it has zero…

In this thesis, we provide an initial investigation into bounds for topological entropy of switched linear systems. Entropy measures, roughly, the information needed to describe the behavior of a system with finite precision on finite time…

Motivated by the notion of topological entropy for free semigroup actions introduced by Bi\'s, we define the Pesin--Pitskel topological pressure for non-autonomous iterated function systems via the Carath\'eodory--Pesin structure. We show…

Let $X$ be a compact complex manifold of dimension $k$ and $f:X \longrightarrow X$ be a dominating meromorphic map. We generalize the notion of topological entropy, by defining a quantity $h_{(m,l)}^{top}(f)$ which measures the action of…

We consider topological dynamical systems given by skew products $S\rtimes_{\tau} T$, where $S\colon Y\to Y$ is a subshift, $\tau\colon Y\to\mathbb{Z}$ is a continuous cocycle, and $T$ is an arbitrary invertible topological system. For…

We introduce a novel quantity for general dynamical systems, which we call the asymptotic uniform complexity. We prove an inequality relating the asymptotic uniform complexity of a dynamical system to its mean topological matching number.…

We prove that the maximal infinite step pro-nilfactor $X_\infty$ of a minimal dynamical system $(X,T)$ is the topological characteristic factor in a certain sense. Namely, we show that by an almost one to one modification of $\pi:X…

Let $f : X\to X$ be a dominating meromorphic map on a compact K\"ahler manifold $X$ of dimension $k$. We extend the notion of topological entropy $h^l_{\mathrm{top}}(f)$ for the action of $f$ on (local) analytic sets of dimension $0\leq l…