Related papers: The interplay between recurrence and hypercyclicit…
Motivated by a question posed by Sophie Grivaux concerning the regularity of the orbits of frequently hypercylic operators, we show the following: for any operator $T$ on a separable metrizable and complete topological vector space $X$…
We introduce a duality triads` notion. These are dual recurrences as used in dynamical data bases theory completed by a third pertinacious relation. Several representative examples of them are given. q-Gaussian triads as well as Fibonomial…
We study the asymptotics and fine-scale behavior of quantitative combinatorial measures of infinite words and related dynamical and algebraic structures. We construct infinite recurrent words $w$ whose complexity functions $p_w(n)$ are…
This paper studies fundamental questions concerning category-theoretic models of induction and recursion. We are concerned with the relationship between well-founded and recursive coalgebras for an endofunctor. For monomorphism preserving…
A methodology for high dimensional causal inference in a time series context is introduced. It is assumed that there is a monotonic transformation of the data such that the dynamics of the transformed variables are described by a Gaussian…
Recurrent connectivity in the visual cortex is believed to aid object recognition for challenging conditions such as occlusion. Here we investigate if and how artificial neural networks also benefit from recurrence. We compare architectures…
The recurrence phenomena of an initially well localized wave packet are studied in periodically driven power-law potentials. For our general study we divide the potentials in two kinds, namely tightly binding and loosely binding potentials.…
We investigate the dependence of Poincar\'e recurrence-times statistics on the choice of recurrence-set, by sampling the dynamics of two- and four-dimensional Hamiltonian maps. We derive a method that allows us to visualize the direct…
We propose a framework for reasoning about programs that manipulate coinductive data as well as inductive data. Our approach is based on using equational programs, which support a seamless combination of computation and reasoning, and using…
In order to understand the long known anomalies in the composition dependence of diffusion and viscosity of binary mixtures, we introduce here two new models and carry out extensive molecular dynamic simulations. In these models, the two…
Using a result of Behrend concerning sets without arithmetic progressions, we construct some examples of dynamical systems with slow time of multiple recurrence. Our theorem is a quatitative analog of Furstenberg's Correspondence Principle.
The compositionality of meaning extends beyond the single sentence. Just as words combine to form the meaning of sentences, so do sentences combine to form the meaning of paragraphs, dialogues and general discourse. We introduce both a…
We discuss the appearance of time-asymmetric behavior in physical processes in cosmology and in the dynamics of the Universe itself. We begin with an analysis of the nature and origin of irreversibility in well-known physical processes such…
The Poincar\'e recurrence theorem shows that conservative systems in a bounded region of phase space eventually return arbitrarily close to their initial state after a finite amount of time. An analogous behavior occurs in certain quantum…
We present a finite-order system of recurrence relations for a permanent of circulant matrices containing a band of k any-value diagonals on top of a uniform matrix (for k = 1, 2, and 3) as well as the method for deriving such recurrence…
Many studies have been conducted on statistical convergence, and it remains an area of active research. Since its introduction, statistical convergence has found applications many fields. Nevertheless, there is a shortage of research…
We introduce a class of linear bounded invertible operators on Banach spaces, called shift operators, which comprises weighted backward shifts and models finite products of weighted backward shifts and dissipative composition operators. We…
We study the discrete-time, real valued bounded process $\{X_n, n\in {\mathbb N} \}$ defined by a second order recurrence relation $X_{n+2} = \varphi(X_n,X_{n+1})$. We obtain the decay of correlations under analytical hypotheses on $\varphi…
In networked systems, the interplay between the dynamics of individual subsystems and their network interactions has been found to generate multistability in various contexts. Despite its ubiquity, the specific mechanisms and ingredients…
The aim of this paper is twofold. On the one hand, we discuss the notions of strong chain recurrence and strong chain transitivity for flows on metric spaces, together with their characterizations in terms of rigidity properties of…