Related papers: Topological entropy, homological growth and zeta f…

In this paper, we develop the notion of entropy for uniform hypergraphs via tensor theory. We employ the probability distribution of the generalized singular values, calculated from the higher-order singular value decomposition of the…

We give a new type of sufficient condition for the existence of measures with maximal entropy for an interval map $f$, using some non-uniform hyperbolicity to compensate for a lack of smoothness of $f$. More precisely, if the topological…

We introduce and study certain topological spaces associated with connected rooted graphs. These spaces reflect combinatorial and order theoretic properties of the underlying graph and relate in the case of hyperbolic graphs to Gromov's…

For Gamma a finite, connected metric graph, we consider the space of configurations of n points in Gamma with a restraint parameter r dictating the minimum distance allowed between each pair of points. These restricted configuration spaces…

We prove that the accumulation points of a sequence of graphs $G_1,G_2,G_3,\ldots$ with respect to the cut-distance are exactly the weak$^*$ limit points of subsequences of the adjacency matrices (when all possible orders of the vertices…

We consider a non-uniquely ergodic dynamical system given by a $\mathbb{Z}^{l}$-action (or $(\N\cup\{0\})^l$-action) $\tau$ on a non-empty compact metrisable space $\Omega$, for some $l\in\N$. Let (D) denote the following property: The…

We prove that for any weakly convergent sequence of finite graphs with bounded vertex degrees, there exists a topological limit graphing.

We prove that to any smooth vector field of a closed manifold it can be assigned a nonnegative number called {\em rescaled topological entropy} satisfying the following properties: it is an upper bound for both the topological entropy and…

In the present paper, we introduce a natural extension of AKM-topological entropy for noncompact spaces and prove a variational principle which states that the topological entropy, the supremum of the measure theoretical entropies and the…

We study the dynamical properties of ball expanding maps, a class of continuous self-maps defined on compact metric spaces. For a ball expanding map, we show that: (1) the set of periodic points is dense in the chain recurrent set; (2) if…

For every $0<\alpha\le\infty$ we construct a continuous pure mixing map (topologically mixing, but not exact) on the Gehman dendrite with topological entropy $\alpha$. It has been previously shown by \v{S}pitalsk\'y that there are exact…

Let $K$ be a complete non-archimedean field of characteristic $0$ equipped with a discrete valuation. We establish the rationality of the Artin-Mazur zeta function on the Julia set for any subhyperbolic rational map defined over $K$ with a…

We study the richness of the ensemble of graphical structures (i.e., unlabeled graphs) of the one-dimensional random geometric graph model defined by $n$ nodes randomly scattered in $[0,1]$ that connect if they are within the connection…

We consider the Tate cohomology of the circle group acting on the topological Hochschild homology of schemes. We show that in the case of a scheme smooth and proper over a finite field, this cohomology theory naturally gives rise to the…

We introduce a notion of graph homeomorphisms which uses the concept of dimension and homotopy for graphs. It preserves the dimension of a subbasis, cohomology and Euler characteristic. Connectivity and homotopy look as in classical…

The entropy of a graph is an information-theoretic quantity which expresses the complexity of a graph \cite{DM1,M}. After Shannon introduced the definition of entropy to information and communication, many generalizations of the entropy…

We study the convexity of the entropy functional along particular interpolating curves defined on the space of finitely supported probability measures on a graph.

We compute the entropy of a closed bounded region of space for pure 3d Riemannian gravity formulated as a topological BF theory for the gauge group SU(2) and show its holographic behavior. More precisely, we consider a fixed graph embedded…

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…

Graphs are a basic tool for the representation of modern data. The richness of the topological information contained in a graph goes far beyond its mere interpretation as a one-dimensional simplicial complex. We show how topological…