Related papers: Tree shift topological entropy
We wish to investigate some elementary problems concerning topological dynamics revolving around our proposed definition of escaping set. We also discuss the notion of escaping set in the induced dynamics of the hyperspace. Moreover, we…
We define a notion of rank for words and subshifts that we call spacer rank, extending the notion of rank-one symbolic shifts of Gao and Hill. We construct infinite words of each finite spacer rank, of unbounded spacer rank, and show there…
The concept of typed topological space is introduced, for which open sets in a topology on a finite set will be assigned types (from lattice). The neighborhood system of a point, the closure and the connectedness can be defined according to…
Topological entanglement entropy, a measure of the long-ranged entanglement, is related to the degeneracy of the ground state on a higher genus surface. The exact relation depends on the details of the topological theory. We consider a…
We compute the topological entropy of the toric code models in arbitrary dimension at finite temperature. We find that the critical temperatures for the existence of full quantum (classical) topological entropy correspond to the…
An evolutionary tree is a rooted tree where each internal vertex has at least two children and where the leaves are labeled with distinct symbols representing species. Evolutionary trees are useful for modeling the evolutionary history of…
We propose a new definition of preimage entropy dimension for continuous maps on compact metric spaces, investigate fundamental properties of the preimage entropy dimension, and compare the preimage entropy dimension with the topological…
We show that the concept of topological order, introduced to describe ordered quantum systems which cannot be classified by broken symmetries, also applies to classical systems. Starting from a specific example, we show how to use pure…
We extend the notion of the geometric entropy of foliation to foliated manifolds equipped with leafwise Finsler structure. We study the relation between the geometric entropy and the topological entropy of the holonomy pseudogroup. The case…
Using only continuous partitions of unity, we provide equivalent definitions for the metric, topological and topological tail entropies and pressures of a continuous self-map of a compact set, as well as their conditional versions. A tail…
We consider labelings of a finite regular tree by a finite alphabet subject to restrictions specified by a nonnegative transition matrix, propose an algorithm for determining whether the set of possible configurations on the last row of the…
We give a "limit-free formula" simplifying the computation of the topological entropy for topological automorphisms of totally disconnected locally compact groups. This result allows us to extend several basic properties of the topological…
We find that the topological phase transition in a chiral ladder is characterized by dramatic signatures in many body entanglement entropy between the legs, close to half-filling. The value of entanglement entropy for various fillings close…
We present a general definition of entropy in the setting of pre-ordered semigroups, extending the notion of topological entropy. From our definition, we obtain the basic properties exhibited by various entropy-like theories encountered in…
The problem of topology change description in gravitation theory is analized in detailes. It is pointed out that in standard four-dimensional theories the topology of space may be considered as a particular case of boundary conditions (or…
The infinite AC ladder network can exhibit unexpected behavior. Entangling the topology brings even more surprises, found by direct numerical investigation. We consider a simple modification of the ladder topology and explain the numerical…
We introduce the notion of a topological symmetry as a quantum mechanical symmetry involving a certain topological invariant. We obtain the underlying algebraic structure of the Z_2-graded uniform topological symmetries of type (1,1) and…
We consider distributions of ordered random vectors with given one-dimensional marginal distributions. We give an elementary necessary and sufficient condition for the existence of such a distribution with finite entropy. In this case, we…
Two flows defined on a smooth manifold are equivalent if there exists a homeomorphism of the manifold that sends each orbit of one flow onto an orbit of the other flow while preserving the time orientation. The topological entropy of a flow…
The network topology can be described by the number of nodes and the interconnections among them. The degree of a node in a network is the number of connections it has to other nodes and the degree distribution is the probability…