Related papers: Statistical Stability for Multi-Substitution Tilin…
In this review we survey the literature on mean-field coupled maps. We start with the early works from the physics literature, arriving to some recent results from ergodic theory studying the thermodynamic limit of globally coupled maps and…
We propose a general framework for constructing and describing infinite type flat surfaces of finite area. Using this method, we characterize the range of dynamical behaviors possible for the vertical translation flows on such flat…
The theory of substitution sequences and their higher-dimensional analogues is intimately connected with symbolic dynamics. By systematically studying the factors (in the sense of dynamical systems theory) of a substitution dynamical…
We develop a theory of operator renewal sequences in the context of infinite ergodic theory. For large classes of dynamical systems preserving an infinite measure, we determine the asymptotic behaviour of iterates $L^n$ of the transfer…
We study Abelian sandpiles on graphs of the form $G \times I$, where $G$ is an arbitrary finite connected graph, and $I \subset \Z$ is a finite interval. We show that for any fixed $G$ with at least two vertices, the stationary measures…
This paper addresses structures of state space in quasiperiodically forced dynamical systems. We develop a theory of ergodic partition of state space in a class of measure-preserving and dissipative flows, which is a natural extension of…
Expanding maps with indifferent fixed points, a.k.a. intermittent maps, are popular models in nonlinear dynamics and infinite ergodic theory. We present a simple proof of the exactness of a wide class of expanding maps of [0,1], with…
The long time behaviour of solutions to stochastic porous media equations on smooth bounded domains with Dirichlet boundary data is studied. Based on weighted $L^{1}$-estimates the existence and uniqueness of invariant measures with optimal…
This study explores the properties of the function which can tile the field $\mathbb{Q}_p$ of $p$-adic numbers by translation. It is established that functions capable of tiling $\mathbb{Q}_p$ is by translation uniformly locally constancy.…
We study the dynamics of a transformation that acts on infinite paths in the graph associated with Pascal's triangle. For each ergodic invariant measure the asymptotic law of the return time to cylinders is given by a step function. We…
Dynamical systems can display a plethora of ergodic and ergodicity breaking behaviors, ranging from simple periodicity to ergodicity and chaos. Here we report an unusual type of non-ergodic behavior in a many-body discrete-time dynamical…
In this second paper, we study the case of substitution tilings of R^d. The substitution on tiles induces substitutions on the faces of the tiles of all dimensions j=0, ..., d-1. We reconstruct the tiling's equivalence relation in a purely…
We prove pointwise convergence, as $N\to \infty$, for the multiple ergodic averages $\frac{1}{N}\sum_{n=1}^N f(T^nx)\cdot g(S^{a_n}x)$, where $T$ and $S$ are commuting measure preserving transformations, and $a_n$ is a random version of the…
We consider the collection of uniformly discrete point sets in Euclidean space equipped with the vague topology. For a point set in this collection, we characterise minimality of an associated dynamical system by almost repetitivity of the…
We study the homogenization of a stationary random maximal monotone operator on a probability space equipped with an ergodic dynamical system. The proof relies on Fitzpatrick's variational formulation of monotone relations, on Visintin's…
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…
We use the swap Monte Carlo algorithm to analyse the glassy behaviour of sticky spheres in equilibrium conditions at densities where conventional simulations and experiments fail to reach equilibrium, beyond predicted phase transitions and…
We use recently introduced notion of stochastic soliton lattice for quantitative description of soliton turbulence. We consider the stochastic soliton lattice on a special band-gap scaling of the spectral surface of genus $N$ so that the…
Let B be a p-uniformly convex Banach space, with p >= 2. Let T be a linear operator on B, and let A_n x denote the ergodic average (1 / n) sum_{i< n} T^n x. We prove the following variational inequality in the case where T is power bounded…
The Euler graph has vertices labelled (n,k) for n=0,1,2,... and k=0,1,...,n, with k+1 edges from (n,k) to (n+1,k) and n-k+1 edges from (n,k) to (n+1,k+1). The number of paths from (0,0) to (n,k) is the Eulerian number A(n,k), the number of…