Related papers: Neutralized local entropy, and dimension bounds fo…
In this article we study $r$-neutralized local entropy and derive some entropy formulas. For an ergodic hyperbolic measure of a smooth system, we show that the $r$-neutralized local entropy equals the Brin-Katok local entropy plus $r$ times…
Ovadia and Rodriguez-Hertz (Neutralized local entropy, arXiv:2302.10874) defined the neutralized Bowen open ball for an autonomous dynamical system on a compact metric space. Replacing the usual Bowen open ball with neutralized Bowen open…
In this note we present a formula for the local metric pressure that generalizes Brin-Katok result for the metric entropy. As an application, we give a straightforward proof of the fact that non-atomic weak-Gibbs invariant probability…
From a geometric perspective, we employ metric mean dimension to investigate the set of generic points of invariant measures and saturated sets in infinite entropy systems. For systems with the specification property, we establish certain…
We quantify the measurement-induced nonlocality [Luo and Fu, Phys. Rev. Lett. 106, 120401 (2011)] from the perspective of the relative entropy. This quantification leads to an operational interpretation for the measurementinduced…
Let $(X, \phi)$ be a compact metric flow without fixed points. We will be concerned with the entropy of flows which takes into consideration all possible reparametrizations of the flows. In this paper, by establishing the Brin-Katok's…
Ovadia and Rodriguez-Hertz defined neutralized Bowen open ball as $$B_n(x,e^{-n\epsilon})=\{y\in X: d(T^jx, T^jy)<e^{-n\epsilon}, \forall 0\leq j\leq n-1\}.$$ We introduce the notion of neutralized Bowen topological entropy of subsets by…
We study the Bowen topological entropy of generic and irregular points for certain dynamical systems. We define the topological entropy of noncompact sets for flows, analogous to Bowen's definition. We show that this entropy coincides with…
We present a new construction of the entropy-maximizing, invariant probability measure on a Smale space (the Bowen measure). Our construction is based on points that are unstably equivalent to one given point, and stably equivalent to…
We present a general approach to the study of the local distribution of measures on Euclidean spaces, based on local entropy averages. As concrete applications, we unify, generalize, and simplify a number of recent results on local…
We introduce the notion of rescaled expansive measures to study a measure-theoretic formulation of rescaled expansiveness for flows, particularly in the presence of singularities. Equivalent definitions are established via…
We extend Bobkov and Chistyakov's (2015) upper bounds on concentration functions of sums of independent random variables to a multivariate entropic setting. The approach is based on pointwise estimates on densities of sums of independent…
We describe a framework in which is possible to develop and implement algorithms for the approximation of invariant measures of dynamical systems with a given bound on the error of the approximation. Our approach is based on a general…
The generalized covariant entropy bound is the conjecture that the entropy of the matter present on any non-expanding null hypersurface L will not exceed the difference between the areas, in Planck units, of the initial and final spatial…
We study the pointwise dimension for a new class of projection measures on arbitrary fractal limit sets without separation conditions. We prove that the pointwise dimension exists a.e. for this class of measures associated to equilibrium…
We consider a randomly forced Ginzburg-Landau equation on an unbounded domain. The forcing is smooth and homogeneous in space and white noise in time. We prove existence and smoothness of solutions, existence of an invariant measure for the…
This paper defines and discusses the dimension notion of topological slow entropy of any subset for Z^d actions. Also, the notion of measure-theoretic slow entropy for Z^d actions is presented, which is modified from Brin and Katok [2].…
For any Bell locality scenario (or Kochen-Specker noncontextuality scenario), the joint Shannon entropies of local (or noncontextual) models define a convex cone for which the non-trivial facets are tight entropic Bell (or contextuality)…
Recently Lewis Bowen introduced a notion of entropy for measure-preserving actions of countable sofic groups admitting a generating measurable partition with finite entropy; and then David Kerr and Hanfeng Li developed an operator-algebraic…
We calculate slow entropy type invariant introduced by A. Katok and J.-P. Thouvenot in [5] for higher rank smooth abelian actions for two leading cases: when the invariant measure is absolutely continuous and when it is hyperbolic. We…