We introduce a pseudo entropy extension of topological entanglement called entropy. Various examples the entropies are examined in three-dimensional Chern-Simons gauge theory with Wilson loop insertions. Partition functions knotted loops directly related to (R\'enyi) entropies. also show that certain setup is equivalent interface two-dimensional conformal field theories (CFTs), and leverage equ...

We study the topological entropy of a particular class of dynamical systems: cellular automata. The topological entropy of a dynamical system (X; F) is a measure of the complexity of the dynamics of F over the space X . The problem of computing (or even approximating) the topological entropy of a given cellular automata is algorithmically undecidable (Ergodic Theory Dynamical Systems 12 (1992) ...

1. Definitions and general properties. Let X be a compact topological space. Definition 1. For any open cover 31 of X let N(ñ) denote the number of sets in a subco ver of minimal cardinality. A subco ver of a cover is minimal if no other subcover contains fewer members. Since X is compact and 31 is an open cover, there always exists a finite subcover. To conform with prior work in ergodic theor...

In this paper we consider the metric entropies of the maps of an iterated function system deduced from a black hole which are known the Bekenstein–Hawking entropies and its subleading corrections. More precisely, we consider the recent model of a Bohr-like black hole that has been recently analysed in some papers in the literature, obtaining the intriguing result that the metric entropies of a ...

such that i) the geodesic flow on MA is (Liouville) integrable by C ∞ first integrals; ii) the geodesic flow on MA is not (Liouville) integrable by real-analytic first integrals; iii) the topological entropy of the geodesic flow Ft is positive; iv) the fundamental group π1(MA) of the manifold MA has an exponential growth; v) the unit covector bundle SMA contains a submanifold N such that N is d...

We consider a random generalization of the classical Fibonacci substitution. The substitution we consider is defined as the rule mapping, a 7→ baa and b 7→ ab, with probability p, and b 7→ ba, with probability 1 − p for 0 < p < 1, and where the random rule is applied each time it acts on a b. We show that the topological entropy of this object is given by the growth rate of the set of inflated ...

Any continuous, transitive, piecewise monotonic map is determined up to a binary choice by its dimension module with the associated finite sequence of generators. The dimension module by itself determines the topological entropy of any transitive piecewise monotonic map, and determines any transitive unimodal map up to conjugacy. For a transitive piecewise monotonic map which is not essentially...

We show that the n center problem in R 3 has positive topological entropy for n 3. The proof is based on global regularization of sin-gularities and the results of Gromov and Paternain on the topological entropy of geodesic ows. The n-center problem in S 3 is also studied.