Related papers: Positive topological entropy and $\ell_1$

We present a statistical mechanical description of randomly packed spherical particles, where the average coordination number is treated as a macroscopic thermodynamic variable. The overall packing entropy is shown to have two…

We survey the connections between entropy, chaos, and independence in topological dynamics. We present extensions of two classical results placing the following notions in the context of symbolic dynamics: 1. Equivalence of positive entropy…

Let $\mathcal{M}(X)$ be the space of Borel probability measures on a compact metric space $X$ endowed with the weak$^\ast$-topology. In this paper, we prove that if the topological entropy of a nonautonomous dynamical system…

The topological entanglement entropy is used to measure long-range quantum correlations in the ground state of topological phases. Here we obtain closed form expressions for topological entropy of (2+1)- and (3+1)-dimensional loop gas…

In this paper, we focus on some properties, calculations and estimations of topological entropy for a nonautonomous dynamical system $(X,f_{0,\infty})$ generated by a sequence of continuous self-maps $f_{0,\infty}=\{f_n\}_{n=0}^{\infty}$ on…

Local and category-theoretical entropies associated with an endomorphism of finite length (i.e., with zero-dimensional closed fiber) of a commutative Noetherian local ring are compared. Local entropy is shown to be less than or equal to…

Let a countable amenable group G acts freely and ergodically on a Lebesgue space (X,mu), preserving the measure mu. If T is an automorphism of the equivalence relation defined by G then T can be extended to an automorphism alpha_T of the…

In this work a deep relation between topology and thermodynamical features of manifolds with boundaries is shown. The expression for the Euler characteristic, through the Gauss- Bonnet integral, and the one for the entropy of gravitational…

For a completely Hausdorff quasi-topological group $G$, we construct a universal pro-$C^*$-algebra $C(E^+G)$ as the non-commutative geometer's analogue of the total space $EG$ of the classifying principal $G$-bundle $EG\to BG$. The…

We produce a probabilistic space from logic, both classical and quantum, which is in addition partially ordered in such a way that entropy is monotone. In particular do we establish the following equation: Quantitative Probability = Logic +…

We show that $C^\infty$ surface diffeomorphisms with positive topological entropy have at most finitely many ergodic measures of maximal entropy in general, and at most one in the topologically transitive case. This answers a question of…

We show the equivalences of several notions of entropy, like a version of the topological entropy of the geodesic flow and the Minkowski dimension of the boundary, in metric spaces with convex geodesic bicombings satisfying a uniform…

In the spirit of topological entropy we introduce new complexity functions for general dynamical systems (namely groups and semigroups acting on closed manifolds) but with an emphasis on the dynamics induced on simplicial complexes. For…

Two new notions of equivalence for representations of a Toeplitz algebra $\mathcal{E}_n$, $n<\infty$, on a common Hilbert space are defined. Our main results apply to $C^*$-dynamics and the conjugacy of certain $*$-endomorphisms. One…

It has been recently pointed out that a definition of the geometric entropy using the partition function in a conical space does not in general lead to a positive definite quantity. For a scalar field model with a non-minimal coupling we…

Given a compact space X and two commuting continuous open surjective maps sigma_1, sigma_2 : X --> X, we construct certain C*-algebras that reflect the dynamics of the N^2-action. When the maps sigma_1, sigma_2 are local homeomorphisms,…

We introduce the $\ell^1$-ideal intersection property for crossed product C*-algebras. It is implied by C*-simplicity as well as C*-uniqueness. We show that topological dynamical systems of arbitrary lattices in connected Lie groups,…

We define a notion of {\it positive part} of a lattice $\Lambda$ and we endow the set of such positive parts with a topology. We then study some properties of this topology, by comparing it with the one of $V^*/\RM_{> 0}$, where $V^*$ is…

Let $W$ be a symplectic manifold, and let $\phi:W \to W$ be a symplectic automorphism. Then, $\phi$ induces an auto-equivalence $\Phi$ defined on the Fukaya category of $W$. In this paper, we prove that the categorical entropy of $\Phi$…

In this paper, we study the complicated dynamics of infinite dimensional random dynamical systems which include deterministic dynamical systems as their special cases in a Polish space. Without assuming any hyperbolicity, we proved if a…