相关论文: Multidimensional local limit theorem in determinis…

In this work we prove the pointwise ergodic theorem for harmonic degree 1 cocycle of a measurable stationary action of Z^d on a probability space. In a precedent paper Boivin and Derriennic (1991) studied this theorem for not necessarily…

In this paper, a polynomial version of Furstenberg joining is introduced and its structure is investigated. Particularly, it is shown that if all polynomials are non-linear, then almost every ergodic component of the joining is a direct…

We prove a Livsic type theorem for cocycles taking values in groups of diffeomorphisms of low-dimensional manifolds. The results hold without any localization assumption and in very low regularity. We also obtain a general result (in any…

In 1975 Szemer\'edi proved the long-standing conjecture of Erd\H{o}s and Tur\'an that any subset of $\bbZ$ having positive upper Banach density contains arbitrarily long arithmetic progressions. Szemer\'edi's proof was entirely…

Given a level set $E$ of an arbitrary multiplicative function $f$, we establish, by building on the fundamental work of Frantzikinakis and Host [13,14], a structure theorem which gives a decomposition of $\mathbb{1}_E$ into an almost…

We consider mutually disjoint family of measure preserving transformations $T_1, \cdots, T_k$ on a probability space $(X, \mathcal{B}, \mu)$. We obtain the multiple recurrence property of $T_1, \cdots, T_k$ and this result is utilized to…

Systems describing the long-range interaction between individuals have attracted a lot of attention in the last years, in particular in relation with living systems. These systems are quadratic, written under the form of transport equations…

Exploiting the equidistribution properties of polynomial sequences, following the methods developed by Leibman ("Pointwise Convergence of ergodic averages for polynomial sequences of translations on a nilmanifold. Ergodic Theory Dynam.…

Nonstandard ergodic averages can be defined for a measure-preserving action of a group on a probability space, as a natural extension of classical (nonstandard) ergodic averages. We extend the one-dimensional theory, obtaining L^1 pointwise…

We investigate ergodic-theoretical quantities and large deviation properties of one-dimensional intermittent maps, that have not only an indifferent fixed point but also a singular structure such that the uniform measure is invariant under…

We prove Lr-estimates on periodic solutions of periodically-forced, linearly-damped mechanical systems with polynomially-bounded potentials. The estimates are applied to obtain a non-existence result of periodic solutions in bounded…

We establish pointwise almost everywhere convergence for the polynomial multiple ergodic averages $$\frac{1}{N} \sum_{n=1}^N \La(n) f_1(T^{P_1(n)} x)\cdots f_k(T^{P_k(n)} x)$$ as $N\to \infty$, where $\La$ is the von Mangoldt function, $T…

Let T be an ergodic automorphism of the d-dimensional torus T^d, and f be a continuous function from T^d to R^l. On the probability space T^d equipped with the Lebesgue-Haar measure, we prove the weak convergence of the sequential empirical…

Let $(X,\mathcal{B},\mu)$ be a probability space and let $T_1,..., T_l$ be $l$ commuting invertible measure preserving transformations \linebreak of $X$. We show that if $T_1^{c_1} ... T_l^{c_l}$ is ergodic for each $(c_1,...,c_l)\neq…

Polynomial Systems, or at least their algorithms, have the reputation of being doubly-exponential in the number of variables [Mayr and Mayer, 1982], [Davenport and Heintz, 1988]. Nevertheless, the Bezout bound tells us that that number of…

Let X be a metric space with metric d and T,S be two commutative measure-preserving maps of X. In this paper we obtain numerical results about multiple recurrence of almost every point of this dynamical system. On other words we study the…

In this paper, for any given polynomial, by analyzing the limiting behavior of ergodic averages along polynomials of several variables and prime numbers, we prove that for a topology dynamical system, positive entropy implies mean Li-Yoke…

We prove a multivariate central limit theorem with explicit error bound on a non-smooth function distance for sums of bounded decomposable $d$-dimensional random vectors. The decomposition structure is similar to that of Barbour, Karo\'nski…

We study the optimization of ergodic averages for multi-valued dynamical systems, i.e. where points may have multiple different forward orbits. Under upper semi-continuity assumptions, we show that the maximum space average with respect to…

We study the probability distribution of the area and the number of vertices of random polygons in a convex set $K\subset\mathbb{R}^2$. The novel aspect of our approach is that it yields uniform estimates for all convex sets…