Related papers: Fourier transforms of Gibbs measures for the Gauss…

Given a space $X$, a $\sigma$-algebra $\mathfrak{B}$ on $X$ and a measurable map $T:X \to X$, we say that a measure $\mu$ is half-invariant if, for any $B \in \mathfrak{B}$, we have $\mu(T^{-1}(B)\leq \mu (B)$. In this note we present a…

We study the Gibbs dynamics for the Zakharov-Yukawa system on the two-dimensional torus $\mathbb{T}^2$, namely a Schr\"odinger-wave system with a Zakharov-type coupling $(-\Delta)^\gamma$. We first construct the Gibbs measure in the weakly…

We give an equivalent condition for the existence of invariant Gibbs measures for sequences of continuous functions on one-sided subshifts and, more generally, for the existence of Gibbs measures. These extend the results of Kim [6] and…

Let $f$ be an entire almost periodic function with zeros in a horizontal strip of finite width; for example, any exponential polynomial with purely imaginary exponents is such a function. Let $\mu$ be the measure on the set of zeros of $f$…

Let $(X, \sigma_X), (Y, \sigma_Y)$ be one-sided subshifts with the specification property and $\pi:X\rightarrow Y$ a factor map. Let $\mu$ be a unique invariant Gibbs measure for a sequence of continuous functions $\F=\{\log…

Let $X \subset \mathbb{R}^N$ be a Borel set, $\mu$ a Borel probability measure on $X$ and $T:X \to X$ a Lipschitz and injective map. Fix $k \in \mathbb{N}$ greater than the (Hausdorff) dimension of $X$ and assume that the set of…

Let $ \tau : [0,1] \rightarrow [0,1] $ be a piecewise expanding map with full branches. Given $ \lambda : [0,1] \rightarrow (0,1) $ and $ g : [0,1] \rightarrow \mathbb{R} $ satisfying $ \tau ' \lambda > 1 $, we study the Weierstrass-type…

The notion of $\ast$-measure on a compact Hausdorff space can be defined for arbitrary continuous triangular norm $\ast$. The well-known Hutchinson-Barnsley theory deals with the iterated function systems (IFSs) of probability measures and…

We propose an extension of ergodic theory which focuses on the identification of ergodicity in terms of the uniqueness of the invariant measure. We first explain the concept for the doubling maps, which can be analyzed using Fourier…

In this work, we are interested in characterizing typical (generic) dimensional properties of invariant measures associated with the full-shift system, $T$, in a product space whose alphabet is a perfect and separable metric space (thus,…

Let d\mu(t) be a probability measure on [0,+\infty) such that its moments are finite. Then the Cauchy-Stieltjes transform S of d\mu(t) is a Stieltjes function, which admits an expansion into a Stieltjes continued fraction. In the present…

We study the dynamics of polynomial-like mappings in several variables. A special case of our results is the following theorem. Let f be a proper holomorphic map from an open set U onto a Stein manifold V, $U\subset\subset V$. Assume f is…

Let $ T:[0,1]\to[0,1] $ be an expanding Markov map with a finite partition. Let $ \mu_\phi $ be the invariant Gibbs measure associated with a H\"older continuous potential $ \phi $. In this paper, we investigate the size of the uniform…

Suppose $\{f_1,...,f_m\}$ is a set of Lipschitz maps of $\mathbb{R}^d$. We form the iterated function system (IFS) by independently choosing the maps so that the map $f_i$ is chosen with probability $p_i$ ($\sum_{i=1}^m p_i=1$). We assume…

We derive a large deviation principle for random permutations induced by probability measures of the unit square, called permutons. These permutations are called $\mu$-random permutations. We also introduce and study a new general class of…

We prove a van der Corput lemma for non-atomic self-similar measures $\mu$. As an application, we show that the correlations of all finite orders of $( x^n \mod 1 )_{n\geq 1}$ converge to the Poissonian model for $\mu$-a.e. $x$, assuming…

In this paper we show that, for topological dynamical systems with a dense set (in the weak topology) of periodic measures, a typical (in Baire's sense) invariant measure has, for each $q>0$, zero lower $q$-generalized fractal dimension.…

We study the "Fourier symmetry" of measures and distributions on the circle, in relation with the size of their supports. The main results of this paper are: (1) A one-side extension of Frostman's theorem, which connects the rate of decay…

By using structural and asymptotic properties of the Kontorovich-Lebedev transform associated with Minkowski's question mark function, we give an affirmative answer to the question posed by R. Salem (Trans. Amer. Math. Soc., 53 (3), (1943),…

We extend the probabilistic approach for constructing Kahler-Einstein metrics on log Fano manifolds X - involving random point processes - to the case of non-discrete automorphism groups, by breaking the symmetry using a moment map…