相关论文: Maximal entropy measures for Viana maps

We introduce a geometry on the cone of positive closed currents of bidegree (p,p) and apply it to define the intersection of such currents. We also construct and study the Green currents and the equilibrium measure for horizontal-like…

We propose an order parameter for a general one-dimensional gapped system with an open boundary condition. The order parameter can be computed from the ground state entanglement entropy of some regions near one of the boundaries. Hence, it…

We prove that if a geodesic flow on a closed orientable $C^\infty$ surface is transitive and has positive topological entropy, then it has a unique measure of maximal entropy. This covers all previous results of the literature on the…

Let $f:X\to X$ be a dominating meromorphic map of a compact K\"ahler surface of large topological degree. Let $S$ be a positive closed current on $X$ of bidegree $(1,1)$. We consider an ergodic measure $\nu$ of large entropy supported by…

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…

Entropies must correspond to mean values for them to be measurable. The Shannon entropy corresponds to the weighted arithmetic mean, whereas the Renyi entropy corresponds to the exponential mean. These means refer to code lengths, which are…

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…

In this note we study some properties of topological entropy for non-compact non-metrizable spaces. We prove that if a uniformly continuous self-map $f$ of a uniform space has topological shadowing property then the map $f$ has positive…

We develop a fine-scale local analysis of measure entropy and measure sequence entropy based on combinatorial independence. The concepts of measure IE-tuples and measure IN-tuples are introduced and studied in analogy with their…

The notion of entropy appears in many fields and this paper is a survey about entropies in several branches of Mathematics. We are mainly concerned with the topological and the algebraic entropy in the context of continuous endomorphisms of…

We introduce a novel entropy-related function, \textit{non-repeatability}, designed to capture dynamical behaviors in complex systems. Its normalized form, \textit{mutability}, has been previously applied in statistical physics as a…

In this paper, we provide an upper bound on the number of maximal entropy ergodic measures with zero Lyapunov exponent for topologically transitive partially hyperbolic diffeomorphisms with compact one-dimensional center leaves on…

A general method for proving continuity of the von Neumann entropy on subsets of positive trace-class operators is considered. This makes it possible to re-derive the known conditions for continuity of the entropy in more general forms and…

The concept of "$A$-coupled-expanding" map for a transition matrix $A$ has been studied as one of the most important criteria of chaos in the past years. In this paper, the lower bound of the topological entropy for strictly…

We introduce a new measure of instability of area-preserving twist diffeomorphisms, which generalizes the notions of angle of splitting of separatrices, and flux through a gap of a Cantori. As an example of application, we establish a sharp…

We provide upper bounds for entropy numbers for two types of operators: summation operators on binary trees and integral operators of Volterra type. Our efforts are concentrated on the critical cases where none of known methods works.…

We propose the use of entropy, measured from the spatial and flux distribution of pixels in the residual image, as a potential diagnostic and stopping metric for the CLEAN algorithm. Despite its broad success as the standard deconvolution…

We classify complex projective surfaces with an automorphism of positive entropy for which the unique invariant measure of maximal entropy is absolutely continuous with respect to Lebesgue measure.

In a recent paper, hep-th/0509109, Gukov et al. introduced an entropy functional on the moduli space of Calabi-Yau compactifications. The maxima of this functional are then interpreted as "preferred" Calabi-Yau compactifications. In this…

We show that the naive application of the maximum entropy principle can yield answers which depend on the level of description, i.e. the result is not invariant under coarse-graining. We demonstrate that the correct approach, even for…