Related papers: Recurrence and algorithmic information
In the study of discrete dynamical systems, we typically start with a function from a space into itself, and ask questions about the properties of sequences of iterates of the function. In this paper we reverse the direction of this study.…
We give a definition of generalized indicators of sensitivity to initial conditions and orbit complexity (a measure of the information that is necessary to describe the orbit of a given point). The well known Ruelle-Pesin and Brin-Katok…
Revivals of the coherent states of a deformed, adiabatically and cyclically varying oscillator Hamiltonian are examined. The revival time distribution is exactly that of Poincar\'{e} recurrences for a rotation map: only three distinct…
Quantitative recurrence indicators are defined by measuring the first entrance time of the orbit of a point $x$ in a decreasing sequence of neighborhoods of another point $y$. It is proved that these recurrence indicators are a.e. greater…
We present an analytical description of the distribution of diagonal lines in Recurrence Plots (RPs) for white noise and chaotic systems, and find that the latter one is linked to the correlation entropy. Further we identify two scaling…
Recurrence behavior of wave packets in coupled higher dimensional systems and periodically driven systems is analyzed, which takes place in the realm of higher coupling/modulation strength. We analyze the wave packet dynamics close to…
Recent advancements of complex network representation among several disciplines motivated the investigation of exoplanetary dynamics by means of recurrence networks. We are able to recover different dynamical regimes by means of various…
This paper presents a new approach for analysing structural properties of time series from complex systems. Starting from the concept of recurrences in phase space, the recurrence matrix of a time series is interpreted as the adjacency…
We review possible measures of complexity which might in particular be applicable to situations where the complexity seems to arise spontaneously. We point out that not all of them correspond to the intuitive (or "naive") notion, and that…
We investigate the convergence towards periodic orbits in discrete dynamical systems. We examine the probability that a randomly chosen point converges to a particular neighborhood of a periodic orbit in a fixed number of iterations, and we…
Recurrence plot is a quite easy tool to be used in time series analysis,in particular for measuring unstable periodic orbits embedded in a chaotic dynamical system. Recurrence quantified analysis (RQA) is an advance tool that allows the…
We study the phase space of periodically modulated gravitational cavity by means of quantum recurrence phenomena. We report that the quantum recurrences serve as a tool to connect phase space of the driven system with spectrum in quantum…
Complex networks are an important paradigm of modern complex systems sciences which allows quantitatively assessing the structural properties of systems composed of different interacting entities. During the last years, intensive efforts…
In this paper we study quantitative recurrence and the shrinking target problem for dynamical systems coming from overlapping iterated function systems. Such iterated function systems have the important property that a point often has…
In this work the dynamics of a spinning particle moving in the Schwarzschild background is studied. In particular, the methods of Poincar\'{e} section and recurrence analysis are employed to discern chaos from order. It is shown that the…
We investigate recurrence phenomena in coupled two degrees of freedom systems. It is shown that an initial well localized wave packet displays recurrences even in the presence of coupling in these systems. We discuss the interdependence of…
In the framework of semiclassical theory the universal properties of quantum systems with classically chaotic dynamics can be accounted for through correlations between partner periodic orbits with small action differences. So far, however,…
We extract the information of a quantum motion and decode it into a certain orbit via a single measurable quantity. Such that a quantum chaotic system can be reconstructed as a chaotic attractor. Two configurations for reconstructing this…
The aim of our paper is to formulate and solve problems concerning multitime multiple recurrence equations. We discuss in detail the generic properties and the existence and uniqueness of solutions. Among the general things, we discuss in…
We evoke the idea of representation of the chaotic attractor by the set of unstable periodic orbits and disclose a novel noise-induced ordering phenomenon. For long unstable periodic orbits forming the strange attractor the weights (or…