相关论文: Recurrence rate in rapidly mixing dynamical system…

The competition between reptation and Rouse Dynamics is incorporated in the Rubinstein-Duke model for polymer motion by extending it with sideways motions, which cross barriers and create or annihilate hernias. Using the Density-Matrix…

We introduce {\it (W')-specification} in terms of language decompositions of subshifts, and show that any recurrence set of a subshift with this property has full Hausdorff dimension. Our main result applies to a wide class of subshifts…

We develop operator renewal theory for flows and apply this to obtain results on mixing and rates of mixing for a large class of finite and infinite measure semiflows. Examples of systems covered by our results include suspensions over…

It is proposed that measurement devices can be modelled to have an open decoherence dynamics that is faster than any other relevant timescale, which is referred to as the ultradecoherence limit. In this limit, the measurement device always…

In this paper we prove two results. First we show that dynamical systems with a $\phi$-mixing measure have in the limit Poisson distributed return times almost everywhere. We use the Chen-Stein method to also obtain rates of convergence.…

A recurrence equation is a discrete integrable equation whose solutions are all periodic and the period is fixed. We show that infinitely many recurrence equations can be derived from the information about invariant varieties of periodic…

A one-dimensional dynamical system with a marginal quasiperiodic gradient is presented as a mathematical extension of a nonuniform oscillator. The system exhibits a nonchaotic stagnant motion, which is reminiscent of intermittent chaos. In…

We consider reversible random walks in random environment obtained from symmetric long--range jump rates on a random point process. We prove almost sure transience and recurrence results under suitable assumptions on the point process and…

It is well-known that orthogonal polynomials on the real line satisfy a three-term recurrence relation and conversely every system of polynomials satisfying a three-term recurrence relation is orthogonal with respect to some positive Borel…

We analyze a class of high-amplitude, high-frequency oscillatory systems in which periodicity occurs on two distinct time scales and establish the convergence of its trajectories to a suitably averaged system by recursively applying the…

Several density-matrix renormalization group methods have been proposed to compute the momentum- and frequency-resolved dynamical correlation functions of low-dimensional strongly correlated systems. The most relevant approaches are…

By considering a counting-type argument on Brownian sample paths, we prove a result similar to that of Orey and Taylor on the exact Hausdorff dimension of the rapid points of Brownian motion. Because of the nature of the proof we can then…

Non-autonomous dynamical systems help us to understand the implications of real systems which are in contact with their environment as it actually occurs in nature. Here, we focus on systems where a parameter changes with time at small but…

We compare the divergence of orbits and the reversibility error for discrete time dynamical systems. These two quantities are used to explore the behavior of the global error induced by round off in the computation of orbits. The similarity…

We study the behavior of dynamical systems under time reparameterizations, which is important not only to characterize chaos in relativistic systems but also to probe the invariance of dynamical quantities. We first show that time…

In this partly expository paper we study van der Corput sets in $\Z^d$, with a focus on connections with harmonic analysis and recurrence properties of measure preserving dynamical systems. We prove multidimensional versions of some…

Recurrent temporal dynamics is a phenomenon observed frequently in high-dimensional complex systems and its detection is a challenging task. Recurrence quantification analysis utilizing recurrence plots may extract such dynamics, however it…

The Collatz Conjecture's connection to dynamical systems opens it to a variety of techniques aimed at recurrence and density results. First, we turn to density results and strengthen the result of Terras through finding a strict rate of…

In the realm of Delone sets in locally compact, second countable, Hausdorff groups, we develop a dynamical systems approach in order to study the continuity behavior of measured quantities arising from point sets. A special focus is both on…

We develop a unified approach for establishing rates of decay for the Fourier transform of a wide class of dynamically defined measures. Among the key features of the method is the systematic use of the $L^2$-flattening theorem obtained in…