Related papers: Recurrence quantification analysis of the period-d…
This paper rediscovers a classical homogenization result for a prototypical linear elliptic boundary value problem with periodically oscillating diffusion coefficient. Unlike classical analytical approaches such as asymptotic analysis,…
We consider the sum of the coordinates of a simple random walk on the K-dimensional hypercube, and prove a double asymptotic of this process, as both the time parameter n and the space parameter K tend to infinity. Depending on the…
We prove the cyclic sum formulas for certain two-parameter multiple series. These are new and non-trivial generalizations of the cyclic sum formulas for multiple zeta values and multiple zeta-star values.
Recurrence plot based measures of complexity are capable tools for characterizing complex dynamics. In this letter we show the potential of selected recurrence plot measures for the investigation of even high-dimensional dynamics. We apply…
In this paper, we introduce the notion of recurrence entropy in the context of nonlinear control systems. A set is said to be ($\tau$-)recurrent if every trajectory that starts in the set returns to it (within at most $\tau$ units of time).…
We prove explicit doubling inequalities and obtain uniform upper bounds (under $(d-1)$-dimensional Hausdorff measure) of nodal sets of weak solutions for a family of linear elliptic equations with rapidly oscillating periodic coefficients.…
Computing asymptotics of the recurrence coefficients of X1-Jacobi polynomials we investigate the limit of Christoffel function. We also study the relation between the normalized counting measure based on the zeros of the modified average…
We consider a class of simple quasi one-dimensional classically non-integrable systems which capture the essence of the periodic orbit structure of general hyperbolic nonintegrable dynamical systems. Their behavior is simple enough to allow…
Through the following, we establish the conditions which allow us to express recursive sequences of real numbers, enumerated through the recurrence relation a_{n+1} = Aa_n + Ba_{n-1}, by means of algebraic equations in two variables of…
We describe new, simple, recursive methods of construction for orientable sequences over an arbitrary finite alphabet, i.e. periodic sequences in which any sub-sequence of n consecutive elements occurs at most once in a period in either…
In the symmetric and the asymmetric trapezoid maps, as a slope of the trapezoid is increased, the period doubling cascade occurs and the symbolic sequence of periodic points is the Metropolis-Stein-Stein sequence and the convergence of the…
A double occurrence word $w$ over a finite alphabet $\Sigma$ is a word in which each alphabet letter appears exactly twice. Such words arise naturally in the study of topology, graph theory, and combinatorics. Recently, double occurrence…
The purpose of this paper is the discussion of a pair of coupled linear oscillators that has recently been proposed as a model of a system of two optical resonators. By means of an algebraic approach we show that the frequencies of the…
In the paper the notion of {\em Rauzy scheme} is introduced. From Rauzy graph Rauzy Scheme can be obtaining by uniting sequence of vertices of ingoing and outgoing degree 1 by arches. This notion is a tool to describe Rauzy graph behavior.…
We discuss how to use the recent progress in understanding of the $x$-$y$ duality and symplectic duality in the theory of topological recursion and its generalizations in order to efficiently compute the quantum spectral curve operators for…
We derive the asymptotic distribution of ordinal-pattern frequencies under weak dependence conditions and investigate the long-run covariance matrix not only analytically for moving-average, Gaussian, and the novel generalized coin-tossing…
This paper is devoted to the structure of the complete asymptotic expansion of the probability that a large combinatorial object is irreducible or consists of a given number of irreducible parts, where irreducibility is understood in terms…
The appropriate selection of recurrence thresholds is a key problem in applications of recurrence quantification analysis (RQA) and related methods across disciplines. Here, we discuss the distribution of pairwise distances between state…
We briefly explore a sequence that came up in recent work of Tirrell and Zhuang. We discover an unusual phenomenon where the sequence appears at first to have periodic behavior but eventually has non-periodic fluctuations.
We derive semiclassical asymptotics for the orthogonal polynomials P_n(z) on the line with respect to the exponential weight \exp(-NV(z)), where V(z) is a double-well quartic polynomial, in the limit when n, N \to \infty. We assume that…