Related papers: On Dynamical Systems With Slow Recurrence Time
We calculate the period of recurrence of dynamical systems comprising two interacting bosons. A number of theoretical issues related to this problem are discussed, in particular, the conditions for small periodicity. The knowledge gathered…
The short time behavior of a disturbed system is influenced by off-shell motion and best characterized by the reduced density matrix possessing high energetic tails. We present analytically the formation of correlations due to collisions in…
We study the time it takes for all states of a finite quantum system to return simultaneously to their original configuration. In particular, we define the recurrence time for a quantum system to be the time at which all time-evolved states…
In the topological dynamical system $(X,T)$, a point $x$ simultaneously approximates a point $y$ if there exists a sequence $n_1$, $n_2$, ... of natural numbers for which $T^{n_i} x$, $T^{2n_i}x$, ..., $T^{k n_i} x$ all tend to $y$. In…
In this paper, we consider the long time asymptotics of multi-time correlation functions for quantum dynamical systems that are sufficiently random to relax to a ``reference state''. In particular, the evolution of such systems must have a…
We develop a diffusion approximation for systems subject to fast random resetting by small amplitudes. Equivalently, this describes systems with frequent but small catastrophes. We demonstrate the validity of the approximation by computing…
This article deals with dynamical systems depending on a slowly varying parameter. We present several physical examples illustrating memory effects, such as metastability and hysteresis, which frequently appear in these systems. A…
We give sufficient Gordin-type criteria for the iterated (enhanced) weak invariance principle to hold for deterministic dynamical systems. Such an invariance principle is intrinsically related to the interpretation of stochastic integrals.…
We show by means of experiments, theory and simulations, that the slow dynamics of coarsening systems displays dynamic heterogeneity similar to that observed in glass-forming systems. We measure dynamic heterogeneity via novel multi-point…
Recent work has generalized the Furstenberg correspondence between sets of integers and dynamical systems to versions which involve sequences of finite graphs or sequences of $L^\infty$ functions. We give a unified version of the theorem…
We describe a mathematical formalism and numerical algorithms for identifying and tracking slowly mixing objects in nonautonomous dynamical systems. In the autonomous setting, such objects are variously known as almost-invariant sets,…
Many dynamical systems exhibit similar structure, as often captured by hand-designed simplified models that can be used for analysis and control. We develop a method for learning to correspond pairs of dynamical systems via a learned latent…
We study a nonconventional ergodic average for asymptotically abelian weakly mixing C*-dynamical systems, related to a second iteration of Khintchine's recurrence theorem obtained by Bergelson in the measure theoretic case. A noncommutative…
We establish almost sure invariance principles, a strong form of approximation by Brownian motion, for non-stationary time-series arising as observations on dynamical systems. Our examples include observations on sequential expanding maps,…
We study non-recurrence sets for weakly mixing dynamical systems by using linear dynamical systems. These are systems consisting of a bounded linear operator acting on a separable complex Banach space X, which becomes a probability space…
Contraction theory for dynamical systems on Euclidean spaces is well-established. For contractive (resp. semi-contractive) systems, the distance (resp. semi-distance) between any two trajectories decreases exponentially fast. For partially…
Starting with a combinatorial partition theorem for words over an infinite alphabet dominated by a fixed sequence, established recently by the authors, we prove recurrence results for topological dynamical systems indexed by such words. In…
The dynamical behavior of a quantum many-particle system is characterized by the lifetime of its excitations. When the system is perturbed, observables of any non-conserved quantity decay exponentially, but those of a conserved quantity…
We establish multiple recurrence and convergence results for pairs of zero entropy measure preserving transformations that do not satisfy any commutativity assumptions. Our results cover the case where the iterates of the two…
In this paper, we introduce the concept of random time changes in dynamical systems. The sub- ordination principle may be applied to study the long time behavior of the random time systems. We show, under certain assumptions on the class of…