Related papers: Form discrete- to continuous-time ergodic theorems

This is an expository article/encyclopedia entry explaining the history, techniques, and central results in the field of smooth ergodic theory.

We prove several extensions of the Erdos-Fuchs theorem.

We survey the classical results of the Dirichlet Approximation Theorem.

We establish results with an arithmetic flavor that generalize the polynomial multidimensional Szemeredi theorem and related multiple recurrence and convergence results in ergodic theory. For instance, we show that in all these statements…

Here we give a short survey of our new results. References to the complete proofs can be found in the text of this article and in the litterature.

Starting with the recursive extended Euclid's algorithm, we apply a systematic approach using matrix notation to transform it into an iterative algorithm. The partial correctness proof derived from the transformation turns out to be very…

We discuss alternative iteration methods for differential equations. We provide a convergence proof for exactly solvable examples and show more convenient formulas for nontrivial problems.

These notes are a self-contained introduction to the use of dynamical and probabilistic methods in the study of hyperbolic groups. Most of this material is standard; however some of the proofs given are new, and some results are proved in…

We give a general method of deriving statistical limit theorems, such as the central limit theorem and its functional version, in the setting of ergodic measure preserving transformations. This method is applicable in situations where the…

We prove a version of pointwise Ergodic Theorem for non-stationary random dynamical systems. Also, we discuss two specific examples where the result is applicable: non-stationary iterated function systems and non-stationary random matrix…

For a differential equation with interaction, we investigate its ergodic properties. We apply the obtained results to study the limiting behavior of braid invariants associated with the flow of solutions.

We present a short proof of Szemer\'edi's Theorem using a dynamical system enriched by ideas from model theory. The resulting proof contains features reminiscent of proofs based on both ergodic theory and on hypergraph regularity.

We review some modern theories about the structure of space and time, in particular those related to discrete space and time. Following an epistemological method we start from theories which discuss discrete space and time as a mathematical…

First, we establish an abstract ergodic result on $\mR^d$. Classical ergodic results on $\mR^d$ require that the process is irreducible, we weaken it to some weak form of irreducibility in this article. The main method used in this article…

We introduce a family of maps generating continued fractions where the digit $1$ in the numerator is replaced cyclically by some given non-negative integers $(N_1,\ldots,N_m)$. We prove the convergence of the given algorithm, and study the…

The purpose of this note is to prove the celebrated Discrete Renewal Theorem in a common special case. We use only very elementary methods from real analysis, rather than markov chain theory, complex analysis, or generating functions.…

Extended Thermodynamics is a very important theory: for example, it predicts hyperbolicity, finite speeds of propagation waves as well as continuous dependence on initial data. Therefore, it constitutes a significative improvement of…

The idea of a parsing of a stationary process according to a collection of words is introduced, and the basic framework required for the asymptotic analysis of these parsings is presented. We demonstrate how the pointwise ergodic theorem…

In this note, we prove or re-prove several important results regarding one dimensional time fractional ODEs following our previous work \cite{fllx17}. Here we use the definition of Caputo derivative proposed in \cite{liliu17frac1,liliu2017}…

We formulate and prove the extension of the Rogers integral formula to the adeles of number fields. We also prove the second moment formulas for a few important cases, enabling a number of classical and recent applications of the formula to…