Related papers: Sublacunary sequences that are strong sweeping out

Consider a mixing dynamical systems $([0,1], T, \mu)$, for instance a piecewise expanding interval map with a Gibbs measure $\mu$. Given a non-summable sequence $(m_k)$ of non-negative numbers, one may define $r_k (x)$ such that $\mu (B(x,…

Linear second order recursive sequences with arbitrary initial conditions are studied. For sequences with the same parameters a ring and a group is attached, and isomorphisms and homomorphisms are established for related parameters. In the…

A speedup, like a time change in discrete time dynamics, is a way of moving faster through the orbits of a dynamical system. Linearly recurrence is a stronger form of minimality for subshifts, shared by e.g.\ all primitive substitution…

Recently, motivated by Stanley sequences, Kiss, S\' andor and Yang introduced a new type sequence: a sequence $A$ of nonnegative integers is called an $AP_k$ - covering sequence if there exists an integer $n_0$ such that if $n > n_0$, then…

The sequence starts with a(1) = 1; to extend it one writes the sequence so far as XY^k, where X and Y are strings of integers, Y is nonempty and k is as large as possible: then the next term is k. The sequence begins 1, 1, 2, 1, 1, 2, 2, 2,…

A sequence $S=s_{1}s_{2}..._{n}$ is \emph{nonrepetitive} if no two adjacent blocks of $S$ are identical. In 1906 Thue proved that there exist arbitrarily long nonrepetitive sequences over 3-element set of symbols. We study a generalization…

Let $a>1$ be an integer. Denote by $l_a(n)$ the multiplicative order of $a$ modulo integer $n\geq 1$. We prove that there is a positive constant $\delta$ such that if $x^{1-\delta}\log^3 x = o(y)$, then $$ \frac1y \sum_{a<y} \frac1x…

The aim of this paper is to investigate the dynamics of a higher order system of rational difference equations. Our concentration is on boundedness character, the oscillatory, the existence of unbounded solutions and the global behavior of…

Let $(X, \mathcal{B},\mu,T)$ be an ergodic measure preserving system, $A \in \mathcal{B}$ and $\epsilon>0$. We study the largeness of sets of the form \begin{equation*} \begin{split} S = \left\{ n\in\mathbb{N}\colon\mu(A\cap…

This paper studies the iterates of the third order Lyness' recurrence $x_{k+3}=(a+x_{k+1}+x_{k+2})/x_k,$ with positive initial conditions, being $a$ also a positive parameter. It is known that for $a=1$ all the sequences generated by this…

Sumsets are central objects in additive combinatorics. In 2007, Granville asked whether one can efficiently recognize whether a given set $S$ is a sumset, i.e. whether there is a set $A$ such that $A+A=S$. Granville suggested an algorithm…

A universally L^1 good sequence n_k is constructed with n_{k+1}-n_k tending to infinity. For ergodic transformations non-conventional ergodic averages of L^1 functions computed by using this sequence converge to the integral of the…

Studying atmospheric escape from exoplanets can provide important clues about the formation and evolution of exoplanets. Observational evidence of atmospheric escape has been obtained through transit spectroscopy in strong spectral lines of…

The Ulam sequence is given by $a_1 =1, a_2 = 2$, and then, for $n \geq 3$, the element $a_n$ is defined as the smallest integer that can be written as the sum of two distinct earlier elements in a unique way. This gives the sequence $1, 2,…

We study sets of recurrence, in both measurable and topological settings, for actions of $(\mathbb{N},\times)$ and $(\mathbb{Q}^{>0},\times)$. In particular, we show that autocorrelation sequences of positive functions arising from…

Let $(a_n)_{n\ge 1}$ be the greedy self-generating sequence defined by $a_1=1$, $a_2=2$, and, for $k\ge 3$, by taking $a_k$ to be the least integer greater than $a_{k-1}$ that can be written as a sum of at least two consecutive earlier…

Let $A$ be a finite multiset of integers. If $B$ be a multiset such that $A$ and $B$ are $t$-complementing multisets of integers, then $B$ is periodic. We obtain the Biro-type upper bound for the smallest such period of $B$: Let…

Let $(x_n)$ be a positive real sequence decreasing to $0$ such that the series $\sum_n x_n$ is divergent and $\liminf_{n} x_{n+1}/x_n>1/2$. We show that there exists a constant $\theta \in (0,1)$ such that, for each $\ell>0$, there is a…

A sequence $\{x_{n}\}_1^\infty$ in $[0,1)$ is called Borel-Cantelli (BC) if for all non-increasing sequences of positive real numbers $\{a_n\}$ with $\underset{i=1}{\overset{\infty}{\sum}}a_i=\infty$ the set…

An infinite sequence $\langle{u_n}\rangle_{n\in\mathbb{N}}$ of real numbers is holonomic (also known as P-recursive or P-finite) if it satisfies a linear recurrence relation with polynomial coefficients. Such a sequence is said to be…